I probably wouldn't use it. The school could alter their scheme any year they want to, even to the point of re-assigning current students new numbers in a new schema. Then there are other possible variables, like what happens if you drop out next year and come back the year after? Now you're 2021-129? 2021 + some new number? I might make it a unique + required index, but not likely the PK since there's no compelling reason to make it a PK when you could use something else that guarantees uniqueness.
The more we hear silence, the more we begin to think about our value in this universe.
Paraphrase of Professor Brian Cox.