I've been looking forward to this game being on speedrun.com, but I don't know how to record on Playstation to submit a run

Easy, game records an hour automatically. Just press tge share button when you want to end the recording, then select save video( the top option)

So when you open a game, it starts the recording?

Also, how would you import that on to your pc when it's done

You can put it on a USB stick, on the video press options on controller to do it