As far as back soreness on a yak, it's all about the seat. A good sit on top yak with an elevated comfortable separate piece seat, it isn't an issue at all, I'd venture to say considerably more comfortable than any canoe I've been in. Like having a lawn chair on top. Important to be elevated, to have your feet below you in my experience. But the sit insides where you sit way low, or the cheaper sit ons with the molded in seats, yeah, they suck on your back and limit mobility in the boat a lot.
As far as standing. I have a Jackson Coosa (the original, not the HD). I can stand. But it's a tweener, when standing I gotta focus on standing, and I struggle to stand and fish at the same time. There are a lot of yaks where standing isn't an issue at all, you could do a little dance on them. But those yaks are heavier and slower to paddle and maneuver in water, they're approaching canoe slow, with a mini bass boat like top. People say, well, put a motor on them. Great for still water with no portages. But running rivers scraping the whole way, and having to portage around dams and such, uh, no. There are also smaller, skinnier, lighter, more maneuverable, faster yaks. You ain't standing on them and they typically have worse seats, no storage, etc. Like I said, mines a tweener that I think is the best compromise for me, there's a tradeoff nomatter how you look at it.
But yaks run the gamet from little whitewater play boats to might as well be bass boats to might as well be canoes, and everything in between. It's a very, very broad category. And I'm seeing more and more stand-up paddleboards decked out for fishing, even with posts and seats on top bass boat style!!! Plus all the inflatables now. On a lake I even saw a paddleboard with an outrigger pontoon for stability. Yak, canoe, jon boat, paddleboard, raft, personal pontoon. The lines are super blurry.
Wider is more stable, more comfortable, heavier, slower. Longer is faster, heavier, and less maneuverable. That's what it comes down to. Pick a width and a length for what you wanna do. Find one with a good seat. And call it whatever you want.