What would you think about converting declaring belote / rebelote mechanism to be more similar to Tysiacha, where you can declare marriage while you're playing the card by pressing shift enter?

Even though this is somewhat rare, some people have difficulty completing belote / rebelote because the next person plays really fast before belote maker can press space. This is especially troublesome for mobile users.

but belot is unique in its way

When you learn a game then you really want to know how it is played in real life so I wouldn't change it. I hope the Rest of belote can be added too.

Hello,
well, in real life, you would put down your card and say "Belote". Another person wouldn't have the opportunity to play faster than you, unless of course you really forgot.

I think that's the main point Sylphrena was making, if you forgot the announcement, too bad, but if you didn't forget the announcement and just weren't fast enough (either because of your connection or because of playing from a phone), then you shouldn't really lose it.
Unlike Uno this shouldn't be a game of speed as much as just making sure that you really want to do it.

When this mechanism was released in Tysiac, I actually wanted to suggest the same, but the main thing that made me not do it is that the rules explicitly say this:

If a player owns the king and the queen of trump, their team can obtain 20 bonus points. To get them, they must announce "belote" when playing the king, and "rebelote" when playing the queen, just after having played the corresponding card but before the next player plays.

If this suggestion were to be implemented, that would invalidate that second part of the sentence, as it wouldn't even be possible for the next person to play before the announcement is made. Personally I don't think that's necessarily a bad thing though, as I think it's more important to make sure the announcement isn't forgotten, rather than you were the fastest person to press Space.

Then I was also thinking that it would probably be necessary to keep backwards compatibility. The reality is that the majority doesn't read the forum or the updates topic (which is itself often not updated), so it would be quite a nasty surprise to find out that pressing space after you played no longer works and you were actually supposed to do Shift+Enter, so you lost it. That's mainly why I'm personally not a big fan of changing something that was established for a longer amount of time, but that's just how I see it.

PS: Shake the device feature may be useful here, except that actually shaking isn't mapped to saying Belote/rebelote in this game.

It's possible to support both methods, people on phone or that prefer it can press shift-enter, long tap, etc, while those used to the original method can press space.

In my experience shaking the device is quite unpredictable and different devices might implement it differently, if they do it at all. Even more danger of unintentionally missing the announcement that way.