They went back in time in several of the different shows and movies.
Once on the original when they went back to assure a space launch and kidnapped a pilot and another one in the movie where they brought whales aboard.
IMO, (yes, I’ve seen the new movie) going back in time DOES destroy the Prime Directive theory.
Kirk stomps on the prime directive almost every episode. Part of the charm for me.
But look. Most of the original episodes don’t make sense in the new universe. In one Spock meets his mother and father. Nope, not in the new universe. All of the episodes with Romulins, wrong. There are no Romulins in the new universe. Kirk fights Spock on Vulcan? That iconic episode can’t exist in the new universe because Vulcan is destroyed.
I’m just saying.