The first major awards that the current crop of episodes will be eligible for is the 2022 Emmys, with nominations announced in July. Most everything else is on a calendar- year basis, so it will be eligible for the 2023 SAGs, Critics Choice, etc.
BTW for those of you wise enough to be watching this show, FYI, that Burlesque theatre being used this season is not a theatre. It is just a set designed and constructed for those amazing scenes!!!!! Nice budget, well-executed.