[2023] Do you keep Temtem Plus if you start a new game?

I bought Temtem for Switch recently. I haven't played it yet or entered the code, so not sure where you enter this but I am guessing it is in the in game store. My question is, what happens if you start a new game after already entering the Temtem plus code - does this get saved onto your Nintendo switch profile, or would it make you pay for Temtem Plus again?

Also, how is the Switch version running for all of you Switch users? I hear that it takes a while to leave combat / enter new areas due to clearing RAM.

TLDR: Does restarting your game mean you need a new Temtem plus code?