There are a few examples of in-universe music in the films and the Rebels tv show (unsure if there are examples in Clone Wars but I would suspect there are)
Cantina Band
The band in the Mos Eisley cantina plays at least two songs that are heard on screen:
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Cantina Band (
in-universe title "Mad About Me")
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Cantina Band #2 (out of universe title)
In Return of the Jedi, from a purely current - Disney canon perspective, there are a few in-universe bits of music played:
Jabba's Baroque Recital
Listed as "source music" (i.e. in-universe) on the 1997 remastered soundtrack. Heard playing upon Jabba the Hutt's introduction. Intended as 'courtly' music for his palace
Jedi Rocks
Performed by the Max Rebo band
Ewok Celebration
We see the Ewoks playing various instruments and celebrating. One can thus assume that the music heard is largely in-universe
Star Wars Rebels (TV Series)
In the episode: The Mystery of Chopper Base, Zeb and Ezra are seen listening to what we would call a stereo and listening to music
https://www.starwars.com/video/star-wars-rebels-leaving-soon
(track titled "Zeb Rock" by Kevin Kiner)
Squid Lake *
Mon Calamari ballet seen in Episode III being performed at the Galaxies Opera House, attended by Anakin and Palpatine. Uncertain if the music in the scene is diegetic or non-diegetic, but, given that the performance is in an opera house and is a pun on "Swan Lake", it may be a given that there is indeed music in the production:
https://www.starwars.com/video/the-legend-of-darth-plagueis
Dex's Diner
Seen in Episode II, there appears to be background source music playing in Dex's Diner that, to my ear, sounds similar to, yet distinct, from the Cantina Band music. This music has of yet remained officially unreleased and unnamed
(fan extracted from film)
Jabba Flow
Heard in Maz Kanata's on Takodana in Episode VII, this piece is source music written by Lin-Manuel Miranda of "Hamilton" fame in collaboration w/ JJ Abrams.
(LMM performing w/ JJ Abrahms)
(the original Return of the Jedi had two different pieces of music instead of the modern Jedi Rocks and Ewok Celebration, called "Lapti Nek" and "Yub Nub" respectively)
Lapti Nek
Sung by Sny Snootles
Yub Nub
Ewoks are shown playing drums and a makeshift xylophone of stormtropper helmets
*hat tip to @PlutoThePlanet for the prequels reminder