The school system has been given enough vaccines to vaccinate the school staff.
Probably not. The school system probably hasn't been given vaccines at all. School systems in the US don't generally have staff trained in administering vaccines. They don't generally have the freezers required to store these vaccines either.
By the sound of it, the school system is probably being told that a vaccine clinic will be coming through schools in some order, or the staff must be organized to come through some other facility.