The Monzo Cash ISA pots are parts of a single Cash ISA account (see Our all-new Savings Pot is here 🎉 [Multiple Instant Access Cash ISA Pots now available!] - #1001), so it would be moving it in and out of the same account.
It is also possible to move money directly between ISA pots. So OP could just open the new pot, transfer the balance from the old one, and then close the old one. Without the funds ever touching the current account/leaving the ISA.