Getting someone’s pronouns wrong once really isn’t too big of a deal. What’s more important is how you react to being corrected and using what they ask you to going forward.
I still don’t know a good way to ask people their pronouns. Or rather I haven’t had to do it often so I don’t have much practice still so I still feel weird. Sometimes I get nervous that asking someone their pronouns might even make them feel like they don’t pass as the gender they want to present as. I’ve talked about this with people and the advice I’ve been given is that the best way to do it is to introduce yourself with your own pronouns. I still haven’t really had much opportunity to do it so not sure how to make it flow conversationally but the idea is that you’re giving everyone the opportunity to do the same plus it lets them know that you won’t react poorly to hearing someone tell you their pronouns.
I’ve really only met one person who prefers they/them and a couple of she/they folks. The trans people I have met all pass well enough in my brain that I don’t have to consciously try to use the correct pronoun. It just takes some effort to get used to.
Back in, say, 2016 or so there was a meme about “did you just assume my gender?” It was always a caricature and it seems like most people either want you to assume it or are okay if you get it wrong so long as you correct yourself once they correct you.