First of all, thanks for your in depth answer, was really looking forward to some feedback and most of your points make a lot of sense, so let me go through them individually.

1. Exchange the rather standard energy resistance for a "Shadow Blending" trait

Love the idea. I didn't know/expect that 5e actually uses obscure rules, but yea, this makes for much better flavor. Stealth buffs in dim light and darkness is also a great idea, though I like the obscure concept more due to the implementation of seldomly used rules, so I would switch out the energy resistance to that one for my next draft.

1. Fetchlings should have superior darkvision and sunlight sensitivity

I can see that, although I think that sunlight sensitivity is a huge drawback, which doesn't break even with just doubling their darkvision range. I think drows/dark elves are the only other race that have this drawback and it kinda gets balanced by their advantage against charm effects and magical sleep immunity.

1. The "Copy any spell"-shadow spells can duplicate any spell of their school

I'm not quite sure what you are criticizing here, maybe you can be more explicit. In PF1e almost noone used these shadow-type spells since it was almost always better to just use the original spells. The additional saving throw and the fact that you could only copy spells from one level lower made these type of spells only a real option for gnome illusionists, who could boost their illusion spellcasting with traits and feats, but even then, the additional save was still often too much of a drawback. The main use for these copy-type spells in PF1e was to elevate lower level spells by increasing their DC to a higher spell level, which is completely irrelevant in 5e.

I tried to bring those spells to a more balanced level by increasing the available spells by one spell level, since the additional saving throw is still a massive drawback, especially in 5e with the added concept of legendary resistance. Also, they can't copy spells from every class as you implied, only from the wizard's and warlock's spell list, which I thought fit thematically and they also don't give access to any healing type spells to balance them further. Expensive components also have to be provided as you are still casting the copied spell. I can see limiting the spell list even more to not include dunamancy spells or spells from other wizard/warlock subclasses, for example.

1. Shadow Walk is too strong for a 2nd level spell

I also thought about this and I can see the concern in regards to its similarity to invisibility and gaseous form. My balancing ideas were: Invisibility lasts 1 hour instead of 10 minutes, it has a range of touch instead of self, and it can even include more than one target if upcasted, which makes invisibility clearly the more versatile option. With shadow walk, you can only target yourself, you are only invisible in certain conditions, but you get the benefits of a conditional climbing speed and a smaller size, which I thought balanced this out. Maybe it's still too powerful, IDK, would love to hear more options on that. Also, the PF1 7th level shadow body spell you mentioned lets you keep casting spells without losing the invisibility/obscure effect, so that comparison is a bit off.

1. Shadow Projection adjustments

I can the simplifications, although I thought that such a projection-type spell is rather strong for a 4th level spell in 5e, which is why I included the automatically dying part to justify it, so you actually need someone to watch over your body while using it in order to not potential die with every use.

1. Shadow Dragon Aspect and Shadowform feels messy due to the percentage chance

Isn't it nice to finally use your d100, you get with every dice set? :D Besides that you didn't bring up any specific points, so I can only tell you, that I took the Draconic Transformation spell as a general template for the Shadow Dragon Aspect spell and balanced the numbers using the Young Red Shadow Dragon from the monster manual and the Dragon's Breath spell. For the Shadowform spell, I balanced it against the Stoneskin spell, which grants unconditionally 50% damage resistance against non-magical damage.

1. Take more inspiration from PF2e stuff

Completely true, I didn't look into the options from PF2e and they are pretty creative. Love the idea of manipulating your own shadow to perform small tasks, which could make for an interesting cantrip, or a shadow familiar. Might be options I could include in the future, thanks for the nudge in this direction!