My pick would have to be the A Whole Nother Story trilogy, in which (spoiler warning) you can only travel back in time. But because time is in a loop of sorts, if you go before the beginning of time, you will be at the end of time. From there you can go back to any time you want to. And time paradoxes cannot be produced. Plus, your memories from the previous timeline exist as well as the memories from the new one.
Dunno if this fits time travel, but I’m happy to see someone else has read it. I think I crushed that book in a single sitting, it’s so good. Try Point B if you haven’t yet.
It sorta fits the brief. Time passes but doesn’t. There’s Definitely travel … I heart crab