I strongly doubt that.

Achievements unlock and sync properly. They also display as they should on both Galaxy and the web profile.
What isn't working is the Galaxy feed. (reached 10h of playtime, achieved 25% of achievs etc).
Web profile feed seems to be working. At least for me and my friends.

EDIT: Not sure if related to this problem but profile backgrounds are also borked when viewed via Galaxy.
Instead of the user chosen one, it displays an image of a castle. Not sure which game it belongs to but it's not from any of mine.

Profile backgrounds display correctly on the web.

Nope. When I go to my profile, my latest achievements are missing (not the activity feed, but the profile). They show in Galaxy tho.

According to the webpage, I got the last one 2 months ago. According to my profile, it was 5 days ago.

However, in that time I only got achievements for one game, so of course it's possible that it's not working for that one game (Beyond A Steel Sky). But personally I doubt it.

Doubtful but not unheard of. Considering the number of games with all sorts of achiev related issues here.
Consider testing a different game to see if they work properly.

I through it was removed intentionally, but didn't think too much about it, even if it appeared to be a nice feature to have.

I feel bad about it, but I still laugh every time I read this XD

Well, we can now say that this is bug #5832 that will never be fixed and archive it.

I'll never forget about that feature.
I really liked seeing achievements on the feed...

My activity feed is completely broken (including "official" Xbox and Epic integrations) since I purchased "Rise of the Triad - Ludicrous Edition" here on GOG.
This game has been patched early on but this problem did not get solved: the issue is that the achievement summary shows 100% but none of the two achievements I really did get are loaded (into the feed or otherwise on the game's Galaxy page). Also my profile page does not show up inside of Galaxy anymore.
The only place where those two achievements do show up is the web version of my profile page - which is still working - but of course only GOG titles (I purchased) are showing up there.
So I don't know if this is the game's fault or a GOG (Galaxy) issue: my feed gets loaded for a very short time but is completely blank afterwards. Yet everything still works on each game's particular page.

For about a month or so my overview on GOG therefore is completely gone and I hesitate on buying anything else anymore.