Can I use my existing password on a new Mac Studio with Time Machine transfer?

Use the password you like and can remember, provided it is not trivial.

If there is a problem with that, the system will tell you.

But generally speaking, you should NOT create a new account at all.

You should simply migrate your data from your old computer, or preferably from the old computer's backup, directly connected to the new computer. The best opportunity to do this is at initial setup.