It’s not widespread BECAUSE Microsoft refuses to include it in all their controllers. It’s been a standard in Sony, Nintendo, and even some 3rd party controllers like 8bitdo.
I’m usually way more into short arcadey yet narrative games like Hotline Miami, but based on your list I’d wholeheartedly recommend What Remains of Edith Finch. It’s a bunch of very short story vignettes, so even if you only have 30 minutes you know you’ll complete one.
Night in the Woods might also interest you. I would always play one in-game day (which is about 1 hour each) to relax before going to bed.