Traveling faster than light would enable sending at least information back in time, violate causality, etc., but I don't remember reading or seeing anything related to it in the Star Wars universe. So, does time travel exist in the Star Wars universe, and if not, how does simple (not wormhole based) FTL travel not violate causality? Is this just handwaved away, or is there an in-universe explanation somewhere?
This is fully covered on Wookiepedia:
While time travel was an exceedingly rare phenomenon, a few cases were partially documented. No record of deliberate, physical time travel is known—all known cases involved unusual hyperdrive malfunctions, the effects of the Force, or similar exotic events.
2.1 Confirmed cases 2.1.1 The flight of the Harbinger 2.1.2 Darth Rivan and the Darkstaff 2.1.3 Bosbit Matarcher, the 225-year-old man 2.1.4 Kinnin Vo-Shay's escape from the Tyus Cluster 2.1.5 The secret of Tet-Ami 2.1.6 The Sooma/Alzar incident 2.1.7 The Bedlam Spirits and Princess Leia 2.1.8 Lak Sivrak's experience 2.1.9 Flow-walking 2.2 Alleged cases 2.2.1 Luke Skywalker's first meeting with his father 2.2.2 The Eternity Crystal hoax 2.2.3 Sam Heggs's account
There are also a couple of time travel instance in non-canon Star Wars material as well
Time Travel now exists in Star Wars canon.
In the recent episode A World Between Worlds of Star Wars: Rebels TV series,
Ezra discovered the entrance to an ancient Jedi temple on his home planet Lothal using which he entered a vast netherworld of pathways and portals. It was a pathway between all Time and Space.
Using a portal in there, he also saved Ahsoka who had previously been killed by Vader: