Why and under what conditions does Q learning converge?

I am looking for a modern proof on why Q learning converges in the tabular setting.

I’ve skimmed the original proof by Dayan and Watkins and I have to say that the terminology and approach are a bit verbose and quickly lost me. I’ve also found some random lecture notes online, but I don’t really trust them. Plus a lot of these uses some martingale, filtration approach which is beyond my knowledge.

Is there any modern treatment for the convergence proof of this very important algorithm?