Achieving a never-ending loop of game tasks
I just want to say that I review C# code style a lot on this site, and this code made me very happy for many seconds, until I spotted this:

public async Task Start(Table t)


So close!

t should, of course, have a much more descriptive name here. You've even done that elsewhere, so it is most likely an oversight on your part.

I don't like underscore notation personally as it smells strongly Hungarian, but it's a commonly-accepted system in C# so I don't have a leg to stand on.