Verdict:
This race is too strong, and includes one ability that, even on its own, is too much to grant to a race.
Explanation:
I'm making a breakdown using this guide for balancing new 5e races. It suggests that on average, a race is about 6 points worth of options. Most of the suggested abilities for your race are listed there, and counting them up, you end up with around 9 points. That means they're on the "very strong side" of races (beating out the Mountain Dwarf, which is currently the most powerful race), and could do with some fewer options. Especially considering I am not counting extra points for flexibility with the skills and +1 ability point.
However, that's ignoring one thing in your race which is incredibly powerful, way beyond anything another race gets (and pretty much forces the race down a single path) and that's the ability to cast the innate spells at your highest spell slot level.
This means that your race is able to cast 3 extra spells at their highest level spell slot every short rest, which is incredibly powerful. No other race has a leveled spell that's available every short rest. No class besides the Warlock even has that, and the Warlock only reaches 3 spell slots per short rest when they hit level 11.
Additionally, as they grow in level, they will ultimately be able to cast 4 9th spells per day, while any other character in the game only gets 1. (And the same applies at lower levels). Since all 3 spells you picked for them to get benefit from being cast at higher level, this is incredibly powerful; way beyond anything what other races grant. It also pretty much forces you down a spell-casting path, as you'll be missing out arguably the most powerful racial trait in the game.
Also, I'm not counting any point deduction for the vulnerability to Radiant damage. The number of creatures in the book that deal Radiant damage is next to none, so that trait isn't to come up very often.
Full breakdown of points
- Ability scores: 3 points (not increasing it for flexibility)
- Darkvision: 0.5 points
- Necrolyte magic: 1.5 points (ignoring the part about the spell slots scaling)
- Necrolyte training: 1 point
- Necrotic skills: 1 point (ignoring the flexibility, again)
- Fetid Attack: 1 point
- Radiant Weakness: I'm ignoring this because it comes up almost never and races usually don't have Weaknesses
- Languages: 1 point for 2 extra languages
- Everything else: 0 points; those are baseline
Suggestions
Definitely drop the scaling spell slots on the spell-casting. I don't think you'll be able to balance that. You should cut down on the superfluous features a bit; I'd suggest dropping the bonus skills, the unarmed attack and maybe one of the languages and/or the Darkvision. Dropping all of those would bring you to 6 points, which is balanced with other races.
Maybe even replace the two languages with "one language of choice". That still gives them a bit of that human flexibility (along with the +1 ability) that comes being based on them, while not making them too strong compared to other races.
I'd also drop the Radiant vulnerability. Not even most genuine Undead have that; it's unlikely to come up, and the one time during a campaign it comes up, it might well end up killing your character (or just being forgotten because it's never come up before.)
No, it is overpowered
As you've stated in your question, you have modeled this homebrew after the Orc and half-orc races.
Half-Orc Race Comparison
Ability Scores - Homebrew race provides a negative modifier to Intelligence. These are normally reserved for monstrous races, but that's okay. Intelligence isn't used that often, so it's a hindrance, but not an enormous one.
Size - equivalent
Speed - equivalent and skill proficiency is similar to menacing trait
Darkvision - equivalent
Undying - this is a pretty big deal that refreshes on short rest. The Half-Orc's Relentless Endurance is your comparison trait, but that only references on a long rest. Being able to do that after a short rest is a big boost.
Immunities/resistance - Half-Orc has none, this is another feature granting significantly more power.
The Half-Orc does have their Savage Attack additional crit damage die, but that only happens on a crit and only adds a single die. It is not equivalent to resistances or short rest Undying.
Orc Race Comparison
Before we get into this specific comparison, there is a caveat that WoTC included in Volo's regarding monstrous races:
Some of these races are unusual in that they have a reduction to an ability score, and some are more or less powerful than the typical D&D races.
Utilizing these as a basis for creating homebrew may not be the best methodology. The comparison above against the Half-Orc may be better or see my note on reskinning of the Warforged Race at the end.
Ability Scores - equivalent
Size - equivalent
Speed - equivalent and skill proficiency is similar to Orc's menacing trait
Darkvision - equivalent
Undying - this is a pretty big deal that refreshes on short rest. It's similar to the Barbarian's 11th level class feature, but without even needing a save. This is likely overpowered.
Immunities/resistance - Orc has none, this is another feature granting significantly more power.
The Orc does have their Aggressive Bonus action trait, but that's granting more movement to move towards an enemy and is much less powerful than either Undying or immunities.
Overall Assessment
The Undying and Immunities traits make this race much more powerful than the comparable races you've modeled your homebrew after and they are not balanced by the minimal impact negative INT score.
If you really want to add the Undying trait, then modelling your design after the Half-Orc will likely give you a better starting point since they have that trait (including the Long Rest refresh only). This would also allow you to remove the negative INT modifier (which isn't really that big of a deal given the small number of INT saves.)
In which case, the equivalent mechanic you're trying to find/create is that of the Savage Attack. However, Resistance to damage is definitely not that and is generally more powerful than an additional damage die you get approximately 1 in 20 attack rolls.
Take a look at the Warforged
As a sidenote, you may want to also look at the Warforged race for inspiration (or reskinning) as these are very similar to what you're describing.
Warforged are formed from a blend of organic and inorganic materials...While they’re formed from stone and steel, warforged are living humanoids.
This very much has a 'created human' feel to it. You'd just be reskinning the stone/steel with some other background fluff.
Best Answer
Overall, Looks Good!
Almost all of these abilities have a precedent. Damage resistance is shared by dragonborn. Proficiency in what is essentially a two handed weapon does not currently exist RAW -Dwarves and Elves are only proficient in 1 handed weapons- but I don't think this is a big deal. Any class that isn't proficient in a two handed weapon probably doesn't want to use one anyway.
Rebalancing of Bear Paws
I agree with Dan B that it would be helpful to parse these out for the sake of readability. I also agree that it's important to prevent the claws from being used as monk weapons. That said, you don't want to remove all flavor: if you bump the bite damage down to 1d6+Str, it will be the same as the Lizardfolk's Bite ability, which is a natural weapon that can be used for monk abilities.
It might also be good to note that these are both "natural weapons" in order to better ground them in the system.
I don't think there's any need to state how many attacks you can make with these weapons per round. None of the natural weapon abilities of RAW classes do this. No weapon description does this. Your claws are weapons, natural weapons - the rules already provide ample guidance on how weapons can be used.
Finally, it is vitally important that you specify that a claw attack requires use of both paws - otherwise, your class could use a shield in one hand and a 2d6 weapon in the other.
Smaller Concerns
The swim speed is perhaps too high, not just from a narrative perspective (a bear that can swim as fast as it can run?) but also because it is the same as the Triton swim speed, and it's probably preferable to not steal the aquatic stage from the fish people race.
From a narrative perspective, I'm curious how the bear can use any weapons at all, but that might be too strong a debuff.
In line with other spellcaster-created creatures from the MM, you might change language from "Common" to "One language known by its creator". Also, maybe "You can speak, read, and with great difficulty write in one language of your creator." would be more appropriate given the trouble using tools?