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.
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
Bear Paws. You have proficiency with your claws and teeth. Your claws
deal 2d6+Str slashing damage and your teeth deal 1d8+Str piercing
damage. Due to your clumsy paws, you can’t use any artisan's tools,
musical instruments, light weapons or finnese weapons.
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?
Best Answer
Overall this race is lacking.
Ability Score Increase: Almost all races get +2/+1, while yours have +2/+1/-2, making this race already weak off the bat. Further, their two increases are for what tend to be mutually-exclusive offensive stats, you either want to be focusing on Str for attacks and wearing heavy armor, or you want high Dex for attacks and to make up for only wearing light armor.
Age/Alignment/Size/Language: not relevant to balance.
Speed: 30 is the average for most other races, so not too strong or weak. Climb speeds aren't common, and this does make them have a slightly better niche.
Darkvision: A fairly common ability, and (if my memory serves me correctly) more races have it than don't. Again, not particularly strong or weak.
Built-in-Armor: Having a minimum armor score that is better than the best light armor you can get (and equivalent to Mage Armor) is pretty solidly good, but not exceptional. Rogues and arcane casters would get the most out of this, while fighters, barbarians, and the like would see little to no use from it.
Ambush Predator: Two skill proficiencies is fairly par for the course, and since Perception is the most rolled skill in the game, and Stealth is probably second or third, so even though they don't get a selection like the Lizardfolk do, these two skills are still very good. Overall these are fairly balanced.
Raptorial Blades/Bug Bite: Giving Raptorial Blades the finesse property isn't something you would normally see on natural weapons, but there are quite a few natural weapons that have rider effects and having finesse in place some other effect is certainly within the bounds of balance. Bug Bite, on the other hand, is entirely a waste. Since it's both weaker than the blades (from a damage perspective, d6 vs d4, as well as because it lacks finesse) and can't be used with Two Weapon Fighting, there's not really a reason to even have the ability, it'll never get used. Drop it and give them something that's actually useful.
Always Watching: This is functionally the same as the elf Trance or the warforged Sentries Rest. Not a particularly powerful ability, this is borderline a "ribbon ability" or that is to say, an ability that exists for flavor purposes but mechanically doesn't contribute much, if anything.
Bottom line, this race is to weak. The relevant abilities are their natural armor and weapon, the skill proficiencies, and the ability score penalty, which overall makes them somewhat lackluster compared to other race options.
This race seems to be intended as a stealthy ambusher who drops on prey from above, likely native to a heavily forested area, or possibly a more arid environment with cliffs, canyons, and mesas. With that in mind, my recommendations are: