Do I need to apply for settled status if I am studying in Scotland, Wales or Northern Ireland?

Yes. Although fees for University may be different in Scotland, you must still apply for the Settlement Scheme to stay in the UK after the transition period ends. Without Settled or Pre-Settled Status, you will have to apply for entry into the UK using the new Immigration System.

See  also this UK Government policy paper on student finance eligibility for the 2021-2022 academic year.