Games are hit or miss, but a lot of them work really well, and they get better all the time. I've been completely happy playing TotK on my deck, with the bonus that I can sync my save between my deck and my PC and then play it on my PC as well, then pick up where I left off on the go.

Depends on the game but some work without many issues

Full disclosure: I didn't use Yuzu while I had my steam deck, too busy working through my backlog of steam games laying in bed. But from what I've read performance seems to be just ok, not good not great not terrible. People are pulling around 20-25fps with I think? dips into the teens occasionally. The rule of thumb IIRC is expect to need 10x the computing power of the thing you're emulating with a mature emulator and I really have no idea if steam deck is powerful enough or not to emulate the switch smoothly even with fully mature software which Yuzu certainly isn't right now. So if you're only going to be playing in handheld it could really could go either way. Alternatively if you're willing to perform some surgery on your joy-cons there's a manufacturer called gulikit that makes hall-effect replacements for joy-cons (IDK where they're sold). I haven't heard of any reviews for the joy-con model but I've heard good things about their equivalent for steam deck's thumbsticks.