I am back again with what must appear a strange question - If we were to stay in Stanza hotel, the only hesitation we have is that there is no fridge in the hotel rooms: I like to take a beer or 2 to my hotel room at night and relax before going to bed. My question is - do corner stores, shops that are open into the evening, sell cold refrigerated beer?

Indeed they do, OXXO, Six, etc all sell cold beer to go. And you buy a cheap Styrofoam cooler and keep some on ice as well. Right down the street from the Stanza on Cuauhtémoc is Madchela where you can pick up some Mexican craft beers too.
https://madchela.company.site/

The hotels I stay at (different part of Mexico) often have no frig in the room. But I have always easily found cold beer either buying it at OXXO or the nearest corner store. Or with a bag of ice (cheap) putting it in a bucket or cooler (or even the bathroom sink) in your room.

Thanks to you both, that could sway me to stay at Stanza Hotel.

There are a couple of OXXO stores within a block or two of the Stanza. Most are opened very late.

We stayed at the Stanza on our first trip to CDMX a few years ago. You may also want to check out the Four Points by Sheraton which is just across the road - they may have fridges!