I mean really, maybe “getting stuck in time loops” is actually a problem of the modern era, so some nice people decided to create these media as an instruction manual in case we do get stuck in time loops… or sent back through time, or parallel timelines, alt-universes, or some other space-time shenanigans, etc…
My favourite was in Orange, a Japanese series about a high school girl who gets letters from the future. It’s revealed in the first episode that the letters really are from her and her classmates in the future, who are trying to prevent the death of one of their own.
Why is spoilers, so…
spoiler
They ultimately fail to change history; however, they also achieve the intended result. In the past, the guy is saved. However, this does not affect their reality; it only creates a new future where the guy lives.
I’m not sure if any other time travel story does it quite like that, I’m sure it isn’t unique to Orange. My favourite film, 君の名は。(your name.) sort of plays with this concept, but you really have to watch it a few times to figure out the timeline(s), and it’s not really meant to be taken that seriously. Some of us in the fandom do, though.