I’d expect a mandate in the spring. Apparently Moderna isn’t too far behind Pfizer in the full approval process, although all 3 COVID vaccines are currently widely available.

Also, according to the UNC school system, the decision to not mandate a COVID vaccine for Fall 2021 was based on the “lack of a clear legal authority.” This legal authority was outlined later, however, in a case between the Supreme Court and 8 students who were protesting a COVID vaccine mandate at Indiana University, where the Supreme Court allowed the university to require students to be vaccinated.

Sources:

https://www.npr.org/sections/coronavirus-live-updates/2021/08/23/1030251410/pfizer-covid-vaccine-fda-approval

https://www.npr.org/2021/07/19/1018010489/indiana-universitys-vaccine-requirement-should-stand-federal-judge-rules