You will definitely need two cats at some point during 13,21, but not before you get to the splitter that has both ends open. I assume then that you're stuck because you can't get your cat up past the first medusa?
You can't go into 13,21 and just start running it, that won't work. There's a little bit of setup to do back and forth between 12,21 and 13,21 relating to to exactly how room transitions behave. (although I suppose it's possible there's a way to get two cats in that I never figured out, and that's actually the "right" way to do it. It's sometimes hard to figure out what's a game mechanic and what's a bug, with how creative the puzzles are 😅)