The undead shadow is literally the humanoid's actual shadow, turned into an undead monster. It is not the humanoid's soul itself.

The Monster Manual entry for the Shadow states:

If a creature from which a shadow has been created somehow returns to life, its undead shadow senses the return. The shadow might seek its "parent" to vex or slay. Whether the shadow pursues its living counterpart, the creature that birthed the shadow no longer casts one until the monster is destroyed.

No

Let's take this feature at a time...

Quick build

This is just flatly wrong. This class is a half-caster, they should not prioritize their casting stat. Glancing down below, this class would always want to prioritize Dex--they are restricted to Light Armor no access to the Mage Armor spell and they don't have Cantrips for steady damage output. So they'll want a high Dex for AC, and to make use of Ranged or Finesse weapons--Str is not a good primary for a class that is restricted to Light Armor.

Proficiencies

Light armor only? This pigeonholes this class into a Dex-build if they want anything resembling durability. They are not a dedicated caster--don't even have Cantrips.

Draconic bond.

Basically a Familiar that can attack at this point. However, unlike a Chain Warlock's familiar, the Pseudodragon does not consume one of your attacks in order to act--as-written, this is a complete secondary character.

Spellcasting

You have the spell range of a half-caster, but weirdly scaling efficiency. Without playtesting, it would be hard to determine how this pans out.

That said, your spell list is basically a grab-bag of the most useful spells in the game drawn from every class's list. Balanced fairly well by the fact that they are mostly (all?) Concentration spells

As an aside--you need to rename this feature. Classes that don't follow the standard rules for spellcasting call their magic feature something else--like a Warlock's Pact Magic.

Fighting Style

You get the same full range of fighting style options as a Fighter does. There is basically precedent for this with a Paladin.

ASI

Normal, whatever, moving on.

Draconic Growth

And here is where the balance starts its nose-dive. Assuming you take a Blue or Gold dragon, you just added a CR 3 companion. At a rough ballpark based on experience, a CR 3 monster is roughly the equivalent of a 4th to 5th level character in combat. So, at 5th level, you are basically controlling 2 characters of roughly similar combat effectiveness.

For comparison, the wolf of a 5th level Beast Master ranger has 1 less AC, 1/3 the HP, and does a fair bit less damage while attacking. And, most importantly A ranger must give up an attack of their own to let their wolf attack. And that's not including the dragon's breath weapon.

I would also note that about this point--your 'pet' is lining up to be as good at Persuasion as your party's social lead unless you have someone with Expertise in Social Skills

Improved Bond

Seems handy in a pinch...not a huge deal, moving on.

Draconic Tendencies

Again, not a huge deal...but I would note there's nothing in there about what to do if you already have the Survival and Nature skills

Draconic Growth

So, the wyrmlings usefulness has gradually been tapering off and keeping it alive has gotten hard. That's gone again.

Assuming you went for optimization and took a Gold Dragon...you are now a level 10 player with a CR 10 companion. Again, based on experience, I ballpark that a CR 10 monster is at least on-par with a level 14 PC. Now you have a pet dropping three (very powerful) attacks per round, as well as their breath weapon--and almost certainly has more hp than your party's Barbarian.

Extra attack

So...now your character is up to 5 effective attacks per round? 2 from themselves, 3 from their Dragon.

Riding Master

A fragment of the Mounted Combatant feat...moving on

Greater Bond

I can see this stacking in pretty terrifying ways. It will always work unless aimed at a creature with Evasion.

Increased Draconic Tendencies

Fluff, moving on

Draconic Growth

Ah-hahahahahahahahahahahahahahahaha

Why are you still in a party? You have a CR 17 companion (significantly more powerful than a level 20 PC) that has Legendary Actions and Legendary Resistance. Other classes get a 4th Attack or regenerating class resources--but you? You get a pet legendary monster.

Subclasses

Weapon Master

Level 3
Seems niche and kinda weird..whatever

Level 7
Eldritch Knights don't get this until level 18

Level 18
Stronger than the Mounted Combatant feat, and that's some pretty serious damage...

Spell Master

Level 3
Okay, now you're almost a half-caster. Still really inefficient

Level 7
The lack of a range on this is questionable--otherwise this doesn't seem too out of place

Level 18
Again, pretty potent, but not nearly as broken as your pet flying apocalypse.

Summary

You have a boss monster as a free-acting companion. There is no possible way this is balanced against the core classes unless the storyline gives them some way to acquire creatures of similar power. Which you could do, of course--but that's not what you asked.

Ultimately, the character themselves is quite lackluster--with underpowered spellcasting, no extra attack until level 11, and being stuck in light armor.

However, they have a boss monster as a pet. The way gameplay with this class would go is that it'd be kinda meh until level 5--then you'd be the strongest character in the party by far. That would then taper off as enemies caught up with your dragon, though you're still controlling 2 full-fledged independent characters--til you had another massive surge in power at level 10 that would largely carry through until max level--with another (frankly obscene) power surge at level 20.