Not totally broken

The easiest way to determine if this is any good is usually to compare to other races - so lets go item by item

Ability Score Increase. Your Constitution score increases by 2, and your Dexterity score increases by 1.

+2/+1 is in line with many existing races:

• Elf: +2 DEX / +1 [INT/WIS/CHR]
• Halfling: +2 DEX / +1 [CHR/CON]
• Dragonborn: +2 STR / +1 CHR

This seems to follow the baseline stats of many D&D races.

Size. Skeletons match the height, but are half the weight of humans. Your size is Medium.

Speed. Your base walking speed is 30 feet.

These are fairly standard, although it is worth noting that some races such as Dwarf/Halfling which have relatively strong features are limited down to 25ft base movement. If you decide that the race is perhaps a little strong this is somewhere I would consider adjusting it slightly.

Darkvision. Thanks to your undead nature, you have superior vision in dark and dim conditions. You can see in dim light within 60 feet of you as if it were bright light, and in darkness as if it were dim light. You can’t discern color in darkness, only shades of gray.

This is quite standard, but it's also worth noting that not all races have access to this. Aarakocra, Human, and Dragonborn do not (although many do). If we determine this race to be quite strong I would consider removing this small feature, to encourage the character to take the light cantrip or carry a torch.

Body Construction. Because of your relentless undead fortitude your body is capable of detatching and reattaching limbs. After a long rest you can choose one of the following abilities:

• Detach Hand.
• Detach Head.
• Detach Arm.
• Attach Extra Bones.

These seem thematically cool, and mostly not too strong. the Detach spells seem mostly like interesting cantrip-level spells as far as I can tell, and add flavour to the character.

Attach Extra Bones Seems more powerful however, and could be quite the boon to certain character types. Gaining AC is generally a powerful effect, many characters carry a shield for +2AC and this means they lose the use of one hand for combat. Dual wielding or using a Duelist style can add +1AC for certain character types which is decent in many cases. For higher level characters this can mean gaining more than the benefit of a shield for free. For a monk character type specifically (who cannot use a shield) this power could be very broken.

I would likely advise removing the AC component of this spell, or making one (or more) of the following changes as a bigger down side related to the bonus:

• Half movement speed
• Disadvantage on stealth checks
• Disadvantage on dexterity saves

False Appearance. While you remain motionless, you are indistinguishable from a pile of bones.

Pretty cool, if your PC gets a chance to use this it will be pretty fun.

Necrotic Constitution. You have resistance to necrotic damage, and you have immunity to poison damage, the exhaustion condition and the poisoned condition. You also have vulnerability to bludgeoning damage.

Having a resistance is usually quite strong but not unheard of. Dragonborn, Dwarves, and Tieflings all have resistances to one element.

Immunity is very strong mechanically, although poison is not the most common damage type from enemies.

Vulnerability is however quite a large risk factor and may help balance out the strengths here. Thematically you may want to consider also including the radiant damage type as another nerf for this character. I might suggest something like this:

You also have vulnerability to radiant damage, and whenever you receive bludgeoning damage you receive an additional 1d8 bludgeoning damage.

Undead Nature. You skirt the line between life and death, you count as both humanoid and undead when it comes to spell effects and abilities. You can’t and don't need to eat, drink, or breathe.

Also quite strong. In a survival situation not needing to eat could be big, however this depends on your DM and how they handle survival.

The main problem here is not needing to breathe - this means that your PC can go underwater indefinitely, and may be immune to the effects of certain gas effects or spells. This could also be totally useless depending on what kinds of challenges the party faces, so it's situational - but in those certain situations it is very strong.

Languages. You can speak, read and write common and one other language of your choice.

Seems quite standard for many races.

Summary

Overall everything here is either in-line with other races, or slightly stronger, or situationally stronger. As the dungeon master, it's up to you to decide what you are happy with. My suggestion would be to make a few nerfs, but I don't think the character is totally broken and I think you could run with it.

My Suggestion:

Definitely do something about Attach Extra Bones, I think the additional AC is over the line and is probably the only thing that really is too much.

Probably choose at least two (possibly more) nerfs to take some of the advantage to disadvantage:

• Lower the base movement to 25ft
• Remove nightvision
• Give disadvantage on stealth checks (skeleton feet probably make a similar noise to walking in high heels)
• Remove some immunity/resistance, or increase vulnerability/extra damage
• Require the PC to breathe
• Lower the ability score increase by 1

It is way overpowered

Base characteristics

In general, 5e races are not that impactful. They give some ability score bonuses, some proficiencies, and some minor benefits. Contrast this with your race which, even disregarding subraces, has two parts that both individually would be stronger than all the benefits of any other race. These are:

You have resistancd Bludgeoning, Piercing, and Slashing From Nonmagical Attacks Not Made With Silvered Weapons.

and

starting at 11th Level, you regain HP equal to 1+your constitution modifier at the beginning of each of your turns.

The first of these is simply very strong, to the point that you take half damage from most attacks, at least in low-level play. The second, apart from giving healing in combat, gives full HP between fights. This is entirely contrary to the design of 5e, which is built as a resource management game, and should therefore under no circumstance include infinite resources (healing). The first has as its closest parallel resistance to necrotic, fire or poison damage that some races get, and the second has no parallel in races at all.

The healing does have some comparable class features, as an 18th level Champion Fighter automatically heals to half health, but note that healing to half health, as opposed to full, does not completely negate health-as-a-resource, as a Champion will still have to use some form of healing (hit dice, healing spells, long rest) in order to attain their maximum survivability. There is also the UA Wild Soul Barbarian who could create infinite resources through its 6th level feature, but this was likely an oversight and will not become an officially published class.

Size, languages, +2 con, speed and age all seem fine to me.

Subraces

The subraces give some normal benefits, such as darkvision and keen senses. These are fine. They also give two more ability score increases, which puts them at the higher end of races. This wouldn't be a problem if it weren't for the other strong aspects.

Hybrid forms

These are very strong, but are not the worst offenders still. Some of them give flying or climbing speed, some give very high natural AC, some give yet more resistances, some give much higher movement, some give advantage on skill checks, and the biggest offenders give pack tactics or bonus action attacks.

This is all too much on an already packed race.

Full forms

Here we let go of all balance concerns.

As an example, the wereboar now has natural weapons stronger than any non-magical weapon (2d8), and it can do an even stronger attack as a bonus action, which not only deals 2d12 damage, but can also displace, prone and curse an enemy. It gets 6(!) more ability score increases, and gets natural armor for an AC of 23 if it has maxed out CON. To top it off, it has poison immunity.

This is all simply too strong. Any part of it on its own would be too strong (except I suppose poison immunity), and all together it is certainly too strong.

The drawback

As for the drawback I largely agree with Dan B's answer, that the drawback mechanic does not work. Indeed, the drawback tends to hurt allies more than the lycanthrope itself. It also gives more work to the DM, who will occasionally have to control a PC, and it also stops happening at some point, as eventually the drawback disappears.

However, although there are problems with the implementation of the drawback, there is also the more fundamental problem that drawbacks don't really work. Consider a theoretical drawback that is both fun and makes the race on average about as good as published races. That means that every combat where this drawback does not trigger or matters less, the lycanthrope is way, way stronger than other party members. If the drawback does inflict its woes, suddenly the party is handicapped to such a degree that they cannot overcome obstacles that they reasonably should be able to conquer. This makes it impossible to balance encounters, and perhaps even worse, puts the lycanthrope in the spotlight all the time, which takes away from the enjoyment of the other players.

You say that you don't want small benefits and drawbacks, but unfortunately that is the only way to make a balanced 5e race.

Comparison to other races

Comparing the lycanthrope to other races directly is essentially impossible, because of the sheer amount of features. So, let's compare the amount of features.

For the amount of features of the lycanthrope, I largely refer to the question and the rest of the answer. There's several features of the base race, combined with complicated rules for (in)voluntary shifting, then there are features for each subrace, for each hybrid form, and for each full form.

Compare this with, say, the tiefling. The tiefling has ability score increases, darkvision, two languages, resistance to fire damage and three spells. That's it. This is roughly the amount of features races have in 5e, and this is what it's balanced for. What you're trying to do is simply impossible.

How to make a lycanthrope

So then, what to do with the idea of making a lycanthrope? I recommend one of two things. First, you could simply redesign it all, placing a heavy emphasis on flavor but being extremely conservative with features that affect combat prowess. Second, you could try making the idea into a class. Classes are "allowed" to be much stronger, as it is where most of the power of a PC comes from. To do so you will still need to scale it down significantly to start with, but with more levels can come more powerful abilities.

Of course, NPC creatures have no real concern for balance, so you could certainly turn it into something to fight against, as opposed to something to fight as.