One other thing you could consider is talking to a local cat shelter about giving an elderly cat a home for the last few years of their life.
I was going to suggest this, too. Adult cats are not a whole lot of work. Mid-life or older cats are beyond the obnoxious teenage years where they tear stuff up, and most of them are content to sleep and keep you company. That's it.
Especially now with clumping litter and
Litter Genie, you don't really have to do much more than scoop stuff out of the box once per day or every other day (depending upon your cat). You can get by with almost never dumping the box entirely and cleaning it out. You just scoop stuff and put it into a sealed container, which is very little effort. If you could get someone to come over and change the Litter Genie bag when it gets close to getting full (with one cat, that would probably take a couple months), that would probably overcome the most work of having a cat.
Edited to add: you do have to add new clumping litter to the box every so often, to keep the litter level up, but you can just pour it in on top of what's still in there. That's a bunch less work than dumping old litter, cleaning the box, and then putting in a whole box full of new litter.
Cats that are indoor/outdoor tend to be even less trouble. They prefer to do their duty outside, and then come inside for food, warmth, and companionship.
Honestly, I don't know how I would have gotten through everything without my kitties and puppies. Having that unconditional love has helped me through a whole lot of grief and despair. It's always helped me when I'm feeling crappy and overtired and isolated and then suddenly some furball comes and starts snuggling me just because I'm there and they love me.
Or sometimes they're just hungry
.
I've almost always had a menagerie which creates a lot more mess (one reason my house is such a disaster, since I couldn't really keep up with it for years), but I also know from experience that just one cat doesn't create much work at all. If Litter Genie had been around back in the day, my house might even be in better shape than it is now.
However, that's just my $0.0.2 based on my own experience. It's worth noting (as you probably already know), that there have been studies that show that pets can help in a lot of not only psychological but physical ways (creation of beneficial feel-good hormones, etc.). But you're the best judge of the reality of what you can do. Just throwing it out there as food for thought.
I hope you're feeling better!