A lot of omegaverses actually insinuate that either both male and female omegas get their mensural cycles (which usually the female ones get it worse or something) OR only female omegas get their periods. I mean, it makes sense when even dogs get their periods and they have to deal with pheromones and shit. I like to think of heat as them ovulating so it happens RIGHT BEFORE their periods.
Authors mostly don't think about women in omegaverse settings. They just... exist. In some versions, the Alpha Women even have dicks - the contrameasure for Omega Males being able to get preggo.
I also think that period would be INSANE, but looking at the fact that I never saw Omega Males described with period - and instead it's just heat and "asshole getting wet" (lmao), i would LOVE for it to be NO periods for Omega Women. PLEASE
Imagen being a omega women, had to deal with period pain AND being on heat??? Hell no i will be on killing spree for the whole month