password of other macbook

I just got a new MacBook M1 Pro, and while signing in to Apple ID, one of the steps is to enter the password for my _other_ MacBook (2013 running Big Sur).

Incidentally I had the same password for both computers, so I entered that password. It then says "enter the password of your OTHER MacBook", as if it recognized and emphasized that I had entered the password of the local computer and not the other one. I tried this several times, making sure I typed it correctly, but same thing.

I then started up my old MacBook and changed the password. Went back to my new MacBook and signed out and in again to Apple ID, and went through the same process. When entering the new password it says it's incorrect, until after X attempts it just tells me I won't be able to fully use my Apple ID account. Clicking on Forgot Password here also just gives me the option of trying again or skipping this entirely, leaving my Apple ID in an incomplete state again.

Now, every time I open Apple ID it persists: Some account services will not be available until you sign in again. But I cannot get past this step due to the problem above...