I'd like to put in a suggestion for a feature that would allow players to have multiple games open on the playroom at a time.
This would be really handy if one game with human players gets really drawn out and I want to pass the time by playing another game with a few bots.

This might be useful, but technically impossible; it would require a quite big redesign of playroom's internals.

Additionally, I don't think it wouldn't be very practical to switch all the time back and forth

You can play with some bots while waiting for your friends, save your table when they arrive, and restore it once they have left.