Hello,
I would like to suppress PR notifying me about the activity of all players, like creating a table, joining a table, leaving a table etc.
Perhaps except notifications related to games I'm interested in like Reversy, Go etc. these are so rare even a notification sound would be helpful so they don't get missed.
But that's a minor thing, I would like to get rid of the general noise in the first place.

I've seen there are multiple channels for notifications in the options. Which-one should I configure?

Hello,
for your particular request, it is global messages.
Disable their speech reading and they will no longer be spoken.

On the Windows client, you can entirely hide them from the history as well. That possibility is currently not available on the web.

Hello,

In addition to Nikola has already said, I must add that unfortunately, you can't filter out all global messages but still keep those related to reversi for example.

It would probably mean a complete reorganization of the channel concept, as well as an advanced filtering feature like those existing in mud clients.
This isn't planed for the moment, but maybe it could be done in the future. I don't know well if the balance between complexity and final usefulness makes it really worth it, especially if we come as far as customizing your own client message classification based on keywords or regular expressions.

Thanks @Nikola and @Aminiel.
@Aminiel doing some development myself I completely understand. Implementing filtering in a way that would look nice and wouldn't be easy to break by the unpredictable users is a drag. :)
Though, this seems like something I could solve on my end. It seems PR uses a hidden div for speaking all the messages. I could write a Tampermonkey script that would disable the aria-live attribute and setup its own hidden container for speech.
Then, whatever would the client pipe into its container, would go through my own filtering and end up being spoken only if it passes. I can add arbitrary effects for various kinds of messages there as well.
There would likely be few ms delay, but in the global space that's negligible, and I can always make the original container live again when a game starts.
Getting the unwanted messages out of the history field would likely need to be a bit more violent, but the same trick should work in principle I think.
Are user-side UI tweaks permitted by the rules?

Are user-side UI tweaks permitted by the rules?

Normally not.