You know not everything is directly about Galaxy. In development, when you have two products (ie the site and client) that do similar things, it makes development easier if you can use a standard code base or feature set in both. This allows issues / bugs, etc to be found quicker and fixed easier as well as not having to duplicate a lot of code or work.

I woudn't be surprised if nearly every feature (where it makes sense) is transfered over from Galaxy to the website or vise versa.

You also want to provide a similar experience so that users know how to use both easily...

Except the site existed before Galaxy and GOG promised that Galaxy wouldn't affect site experience so unless I'm mistaken transferring features from Galaxy to GOG is not same as it would be the other way round.
Edit: To explain further this update has broken chat on tablets, and notifications are broken for messages or game updates for some time now.

Edit 2: I've actually reconsidered my complaints, after getting those shortcuts (notification bell and friends thing) it's usable now at least.

I don't know where GOG ever "promised" that... but I doubt you will be able to hold GOG to any statments about Galaxy or the site indefinitely. Sooner or laters things change. They have too.

Not impacting the site experience could simply mean not changing how things are currently handled (ie standalone installers). Doesn't mean features won't change. A site doesn't keep the same features or how they are currently implemented forever.

So

If a change is made to Galaxy only, but not the site, people complain that only Galaxy is being updated and website is different from Galaxy.

If a change is made to Galaxy and to the site, people complain as well that website is just like Galaxy.

All we've got now is what we already had, only less convenient, and what was broken is still broken. I think I'd be happy leaving those kind of updates to Galaxy :P

EDIT: Sorry, my bad. Apparently the notifications are back!

If a change is made to both Galaxy and the website, people complain as well that the website is becoming Galaxy.
If a change isn't made to Galaxy people complain Galaxy isn't improving.
If a change isn't made to the website people complain it isn't improving.

Thus mathematically speaking we can derive a core truth: People complain. :)

I think that's the principle GOG has realized and operate under, that people complain no matter what so just do what we're going to do and move on. If something catches on fire big, put the fire out with minimal fire extinguishers necessary and then go back to task once the shouting drops below N decibels.

In addition to what Hypersomniac mentioned, I find it terribly annoying how the users I blocked are now dumped together with all the ones I talked with instead of being at the bottom of the list (and are not even in any way marked on the list as blocked), and the drop-down menu holding the list of users only shows five at once. It all makes finding someone needlessly bothersome.

So the new chat (and notification system) shows users online on site & galaxy, only online in galaxy or only online on site?
Also, how does it lists users who "appear offline" or have not been active on the page for a while (that may be several hours)? How about if one starts a game then disconnects - does it lists him in the game or offline?

The GOG chat is mainly useful for passing game keys to contest winners and similar. Any chat beyond that is IMHO best done using Discord these days. The IM chat built into pretty much all gaming clients sucks these days and there isn't much incentive for any game client provider to fix them IMHO.

Even GOG devs themselves use Discord (based on photos they've posted in the past). :)

Holy ####! I just saw notifications!

P.s: please, we don't need them blinking in the tab title though

Hee, I got finally some notifications :)
Well done GoG, well done.