Any ideas on how to recover my Time Machine backup with a lost password?

I am trying to migrate my Time Machine backup to a new Macbook, but lost the Time machine administrator name and password.

My old Macbook still connects to Time machine, so the information (administrator and password) is in that computer somewhwere - I just can't find it.

Is there a way to find that information in my old machine or otherwise get into the Time Machine files?

I am using a Seagate external drive connected to a wireless router.