What’s a word, phrase, or expression that means to get together with people informally to play music? Something that doesn’t imply any particular style — could be Jazz, Rock, Classical, Rap, etc.
It is called a jam session. It is sometimes shortened as jam. (jam is used as a verb as well.)
An informal gathering of musicians to play improvised or unrehearsed music. [TFD]
I don't think you'll find a term that is completely devoid of genre context; though I agree jam is the most widely-applicable.
One term a bit more in the vein of classical music would be a reading session. It's semi-formal, since it's not a performance and the participants are usually volunteers, but there will still be a conductor and perhaps a librarian facilitating. The purpose is to play new music to test it out for the music director or even the composer. The term is also used in styles other than orchestral, like jazz big band or classical chamber music.
Another option in the informal sphere might be a hang. As in, "the cats are going to hang at Miles' place after the gig" as a verb or "meet me at the hang after the gig" as a noun. But the playing of music is not necessarily required or assumed with this term like it is for the others--at best it can be defined as "socialize".
There doesn't seem to be a word that ignores how you are going to play the music together, so which word you use depends on how you will play.
If you're going to be emphasizing improvisation, you could call it a "jam". If you're going to be reading music together, you could call it a "reading session". If you're going to take turns playing something with other people following along, you might call it a "session" (without "jam", because you're all playing the same thing, more or less - Celtic music is often played this way in impromptu groups).