Would be great ;)
Ps: Fix the photo mode bug.

I'm actually also kinda curious about achievements, usually I'm not an achievement kind of guy but maybe for certain kinds of games it is nice, although if the release itself did not include achievements I doubt they will implement it suddenly in the future, I haven't seen anything like that before at least.

Well, it's indie title. They also are yet to include ingame (!) screenshot support. So there is still hope.

Frankly, this is a very weird release.
The game already has achievements on Steam, so adding achievement support in GoG should be as simple as using the GoG API in the GoG version, but they're not doing it.
Furthermore, the game has already had several updates on Steam, yet not a single one on GoG.

It kind of feels like they don't care about the GoG version. Why did they even release one?

You might find some answers in these two posts:
#1
#2

As for the release... They probably ran out of money and needed to release in order to continue development. (Which would also explain why the OST wasn't included with the game.)
And while A Hat in Time is still in beta, it's still a good game. It's currently overpriced - considering the length, the performance issues, occasional camera glitches, missing features*, ... - but for all intends and purposes a good game. If they would be selling it for 11 USD I would have bought it even in the state it's currently in.

And just a quick footnote: I don't consider price tags when talking about the quality of a game. Those just make a good or bad value proposition - never a good or bad game.

* "A Hat in Time is releasing with full modding, an in-game screenshot mode, and more!" I don't know what "and more" is, but screenshot mode is broken and modding seems to be missing as well.