Other than very thorough sanitisation measures, wearing masks in communal areas (not in class), large gatherings happening online, the idea of effective social distancing in school has otherwise been pretty much non-existent tbh. It's just not practical in day to day activities so the possibility of infection is still rife in schools imo. It makes sense for all teachers to be offered the vaccine.
Having said that, if all vulnerable people have been vaccinated then in theory it shouldn't really matter.
On an another note, what I think is the bigger concern is the rates at which this virus is mutating and the number of gene mutations that occur with every variant. The South African and Kent variants were just the beginning. Now reports of further variants, including ones which combine the gene variations of both. The unknown is how many of those are a "variant of concern" and how many affect the spike protein which increases rates of infection. And of course how susceptible they remain to the current vaccines.