Spellcasting
The sorcerer spell list is significantly more damage-focused than the druid list, which tends towards debuffs and utility spells. That doesn't make it inherently unbalanced as such, but it might be of concern. I might suggest using the druid list, and if there are a couple of specific sorcerer cantrips or spells that seem particularly apt for the character, add them to his list, rather than just switching out the entire spell list. It only takes one or two cantrips to give the character a unique flavor, without going to the extreme of rewriting the whole class list.
Wild Shape
Switching Wild Shape into, let's call it "Monster Shape", is a tough question. Honestly, it really does depend on which subclass he takes, because a Moon Druid's expanded CR choices will make all the difference.
A non-moon subclass may find the monster choices very limiting, because there just aren't that many weak monstrosities that don't have a fly speed. I think you'll find that at 2nd level (CR 1/4) he'll have no valid choices, and only a handful at 4th level (CR 1/2). This may, of course, change with future book releases. Once he hits 8th level there are maybe a few interesting Monster Shape forms, but still very limited, and weak for that level to boot. A normal non-moon druid at that level tends to use wildshape for utility effects rather than to get cool combat forms, and some of that utility will be lost just because a Darkmantle or whatever is a lot more notable than a raven, rat, or even bear.
Using Circle of the Moon adds quite a few forms. It's still very limited, but maybe not so bad; the big issue there is as you level up, you'll be adding monsters with bizarre abilities to the list, some of which are fine for their CR in the context of a single fight but may be gamebreaking if a PC can just use them any old time he wants. Most of the really bad stuff is forever out of reach, but at higher levels you will see stuff like Lamias, Gorgons, and Medusae coming into play. And Mimics are in at 6th level, which all by itself might give you pause.
So what can you do? Well, I feel people often try to over-complicate things by rewriting huge swathes of rules text to fit with a weird idea, rather than taking the safer and easier path of reskinning the existing rules with new descriptions to match the flavor of what they want to do, and possibly making one or two little tweaks when the mechanics don't quite work as written.
My suggestion in this case is to use Wild Shape as it's written, but change the flavor by reskinning each of the Beast forms to describe some quasi-human monstrosity instead. A dire wolf becomes a hulking wolf-man. A giant eagle becomes a harpy or even griffon form. A warhorse form is described as a centaur or minotaur, a brown bear is an owlbear or half-troll, a giant bat is the Man-Bat from DC Comics. Whatever. I think that sort of thing could easily give you the flavor of turning into bizarre monsters without getting into the mechanical difficulties of the actual Monstrosity creature type. (You'll still have the roleplay effects of being a gross monster rather than just a regular horse or what-have-you, so this might work best if he goes for Moon druid.)
The only mechanical changes that might come up are whether some monster forms can talk or use their hands, but even then it's less common than it might look. A giant wolf-man that's secretly a direwolf probably can't speak like a human, just growls and howls, and his massive clawed hands could easily be useless for anything but the most basic grasping that a wolf's muzzle could accomplish just as easily. You could have his forms use the "monstrosity" type rather than "beast" -- the only real game effect there is immunity to a tiny list of spells and effects. ("Animal Friendship" and "Dominate Beast" are the only ones that really come to mind, off the top of my head, and those can be largely duplicated by higher level spells -- they're just easier to get to if you're targeting a beast.)
It's probably too strong
Firstly let's compare to what other 1st level domains get.
- Arcana: Arcana proficiency, two Wizard cantrips
- Death: Two martial weapon proficiencies, Reaper*
- Forge: Heavy armor proficiency, smiths tool proficiency, Blessing of the Forge*
- Grave: Circle of Mortality*, Eyes of the Grave*
- Knowledge: Two ability proficiencies
- Life: Heavy armor proficiency, Disciple of Life*
- Light: Light cantrip, Warding Flare*
- Nature: One druid cantrip, one ability proficiency, heavy armor proficiency
- Tempest: martial weapons proficiency, heavy armor proficiency, Wrath of the Storm*
- Trickery: Blessing of the Trickster*
Domains that only get cantrips and proficiencies are definitely worse than your proposed feature, so lets compare with Death, Forge, Grave, Life, Light, Tempest and Trickery. But first...
About spiritual weapon:
Is it better than one attack per round? Well yes and no.
- It uses your spellcasting ability modifier, this could be better or worse but it's certainly different.
- It is a second level spell, that lasts for one minute
- You can't cast an action spell on the turn that you use spiritual weapon
Because it is a second level spell, it is a limited resource that you can't have forever. When a typical cleric decides to cast spiritual weapon, they can't cast an action spell that turn which limits their action economy.
With your proposed feature the extra attack itself doesn't cost any resources. While you do need to use resources to activate it, those resources still do whatever they would have done otherwise - making the extra attack free.
Why is this feature too strong compared to...
As you've explicitly mentioned, what do higher level clerics tend to do with their actions? Cast a lot of spells. So what do they usually do with their bonus action? Not much. They might be using spiritual weapon, however that comes at the cost of spell slots and not being able to cast an action spell. Typically a Cleric won't use their bonus action much of the time.
This ability affects the action economy quite significantly, giving the cleric with this ability a large number more attacks per long rest than most other cleric types.
Compared to Death Domain
Reaper allows the cleric to cast a necromancy cantrip at two targets instead of one, as long as they are next to each other. This might be the closest comparison to your feature however it's definitely not as strong. The effect only triggers in specific scenarios (compared to almost always) and when it is used, the caster must spend their action on a cantrip which is not an overly strong manoeuvre.
Compared to Forge Domain
Blessing of the forge allows you to add +1 to a weapon or armor, which is OK in the early game but quite insignificant in the long run.
Compared to Grave Domain
Grave domain has a significantly better save the dying cantrip, and better healing on restoring creatures from 0. They can also sense the undead. Neither is particularly game-breaking and both are situational.
Compared to Life Domain
Extra healing on spells, nothing too noteworthy here.
Compared to Light Domain
Gets an extra reaction option to give an enemy attack disadvantage, can be useful but reactions are limited resources. You can only use this as many times as your WIS mod.
Compared to Tempest Domain
Gets a reaction damage option. Reactions are limited resources, and you can only use this as many times as your WIS mod.
Compared to Trickery Domain
Can give a creature advantage on DEX saves for an hour, not gamebreaking.
tl;dr - Summary
I think this ability is too strong and versatile into the late game. Most of these other level one features are good or OK in early game and much worse later. The best ones are situational and this ability is almost always good.
My Recommendation
If you cast a spell with a spell slot of 1st level or higher and an ally is one of the targets of the spell, you can make one weapon attack as a bonus action. You can use this feature a number of times equal to your Wisdom modifier (a minimum of once). You regain all expended uses when you finish a long rest.
Best Answer
Summary
A Necromancer of the Creed of Tomes is balanced, any other is over-powered.
Base Class: Balanced
The base class is very similar to a Bard: it has the same number of Spells known, for example.
It has only one more Cantrip, at the cost of a lower hit die (d6).
Its Vitality Shift is interesting. The fact that it can transfer up to 400 Hit Points at level 20 may be scary, but on its own this feature is not a problem due to the limited number of uses per day -- up to 5 -- and the fact that it is a transfer: any Hit Point taken from another must still be healed, in the end.
There are a few potential for abuses. A horde of followers is the obvious one, but the DM should be able to curtail that quickly.
Eternal Youth is on the powerful side. Few classes gain Proficiency in a second major Saving Throw. If the character also takes the Resilient feat for Dexterity, this leads them to covering all 3 major ones, and therefore being a bit of a pain to deal with. It comes online at level 18, though, when the character already has access to 9th level spells...
Creed of the Departed: Overpowered
The Undead Minion feature is hard to judge, due to its open ended nature, although there are good limits in place:
Even the Conduit Walker feature is clearly copied from the Find Familiar Spell: same range, same use of Reaction.
The Sheperd's Resolve lifts the speed penalty, and adds another 1d6 of Hit Points to the Undead Minion. Both are minor gains.
The Animator Style is concerning, or at least 2 out of 3 options are:
Still Life is a ribbon; little enough mechanical effect.
And Legendary Animator causes concern again, building upon Animator Style: 6 Huge Creatures will cause a lot of mayhem...
Creed of the Siphon: Overpowered
Sycophant is problematic. There is no other feature in the game which does not place a limit on the amount of Hit Points one can heal. For example, the Champion's capstone ability only heals them up to 50% of their Hit Points. Also, in combination with Vitality Shift it allows regenerating a significant portion of the party Hit Point pool.
Learned Siphoner is also problematic. First of all Necrotic is not as oft resisted as non-magical damage, or even Fire and Cold, so the ability to have a Fireball deal Necrotic damage is problematic in and out of itself. Worse, though, is that it compounds with Sycophant: 1/3 of the newly dealt damage heals the Necromancer after all...
The sub-features of Learned Siphoner are mixed:
Ascetic Dominion offers cheap resurrection. By level 10 some forms of resurrection are available already, and the level of exhaustion suffered prevents really jumping back into the fray. I could foresee mass-resurrection abuse: resurrecting an entire village, 1 Hit Point per villager. Whether that can really be exploited is less clear, however.
Everlasting is one of many abilities to thwart death available to players; once per Long Rest is definitely fine.
Blood Funnel is concerning due to its ability to steal Hit Points from foes; but given Sycophant it doesn't add much...
Note: I couldn't see all the text for Blood Funnel, due to formatting issues and apparently a "cut" copy/paste; I may have missed something.
Creed of Tomes: Balanced
Initiate of the Tome is fine. The Refined Spell is the only powerful feature, and it's a once per Long Rest one.
Arcane Shift is once again a transfer, so none too problematic, especially given the 1 Spell Slot per shift combined with the limited number of possible shifts.
Evercasting is a good capstone. It should not kick in too often, due to the (cumulated) CR 10 requirement, and its limitation to lower-level Spell Slots limits abuse: Action Economy dictates that again powerful foes, the higher-level Spell Slots will be the most necessary.
The Augur's Acumen really depends on the Acumen. Of interest, there is no possibility to switch a known Acumen for another, hence it is not possible to end up with all high-level Acumen and no low-level one.
I noted 2 interesting Acumen, which I think could be accidentally construed as more powerful than they are:
Overall, I find Augur's Acumen fairly balanced.