Quitter I've never seen a gigging musician in these genres play from sheet music. You're expected to play from memory. No one will hire you if you don't know the standards from memory.
I've occasionally had a lead sheet in front of me "just in case", especially doing 3 or 4 hour gigs where there are no repeats and we're doing a number we've not done in public before. Something to jog my memory of how a B section starts off, something like that. But typically, I have a set list with song titles, a key, a tempo, typical play time, and sometimes a few words to help me remember something such as "two tags on the end" or some such. For the most part, I'd be fine with someone just calling out the songs. But there might be a handful that I might mess something up pretty easily, like playing it in G instead of F (I did that once, no one knew except the bass player. LOL! I started it in the wrong key, but hey, it wasn't that hard of a song, so I just kept on going. Didn't figure there was any need to shut it down just for that, and I didn't. )
I think I have maybe 70 or 80 songs in my head, most are in the Real Books so I've got some more learnin' n memorizin' to do. Probably pick up a dozen or so new ones a year without even trying. And sometimes the guys on YouTube who do tutorials have some good tunes they go through that I didn't know. I've got "Bernie's Tune" in my head right now and that came from a tutorial, I'd never heard it before. Snappy little tune.