Hello,
it is basically not related at all and is probably better for a separate topic, but anyway I'll try to respond:
The first thing I can think of is that some browser and screen reader combinations do not allow the same thing to be announced more than once with ARIA live regions (a technique used by websites to automatically announce messages to the screen reader).
For example, this can be observed with Chrome and NVDA. If you press W to hear who is at the table, and then press W again with no new messages spoken and with no changes to the number of people on the table, this will no longer be announced. To have it announced again, you must cause some other message to be spoken by pressing some other information key.
That's a limitation by the browser to prevent abuse by some other websites which use this method incorrectly and cause lots of unnecessary messages to automatically be spoken.
Testing your scenario right now with Chrome and NVDA, for some reason this seems to be even more enforced now, the G key indeed causes problems, even if you hear many other messages inbetween.
However, if nothing is announced, it means that the content did not change since the last time you pressed G. In my testing, pressing some other key like T and then G helps, but if other game messages arrive in the meantime this doesn't seem to solve the problem without first pressing another key and then G later.
This is my theory only for the G key, for R, it's something different I believe:
The R key opens an input dialog to raise your bet. Once you are done with this dialog, it has to close, and the focus has to return to the game.
However, on the Web, it isn't so simple to ensure that the message about your bet raise will be spoken in this case, because sometimes the screen reader will first announce the focus change and then the spoken message, sometimes the message comes a little sooner so the focus change will interrupt it, but this also partially depends on your connection speed.
This one shouldn't be such a big problem, you can already confirm by how much you are going to raise before closing this dialog.
Either ways, unfortunately there is no magic solution I can give here, you may try to experiment a little with the speech priority option inside options/channels and views/game messages. A higher priority may work better with some screen readers, but it is probably going to interrupt what is being read as soon as a new message arrives.