Welcome to the forum, from SE Wisconsin.

The backside being sore quickly is 1/2 the saddle and 1/2 your butt being acclimated. That Selle Royal saddle you've got is generally considered a good one for hybrid bikes like that. A recumbent bike will move ALL your body weight to your back and backside, so it will 100% solve your wrist problem. However, be aware that (in addition to the expense) recumbents can be hard to move around without a truck or full size SUV.

Re. wrists being sore, you can likely address this by replacing those junk grips with ergonomic ones. Ergon out of Germany is the popular and high quality name brand. You can get them with "bullhorns" on the ends too, to give you another hand position. I find that helps a lot. The bar is already pretty high, but the stem you have fitted there has it pretty far forward. You could replace the stem with one that is high, but not so far forward, which will move some weight from your wrists to your butt.

The more weight you move from your wrists to your butt, the wider the saddle should be, so you might need a wider saddle too.

Still, a new stem and wider saddle are a LOT cheaper than a recumbent bike.

I'm a big fan of eBikes; I have four of them and four muggle bikes. You might want to look at Trek's Verve+ line. (where the "+" indicates electric assistance) They're pretty upright and are "bike shop quality. You can do as much or little work as you're in the mood for, and it's adjustable to do nothing. The bike is heavier than a regular one, but not so much that you can't pedal it unpowered.

Enjoy your stay. Maybe we'll see you in the Electric Bikes subforum soon.