The bad omen effect is not shown in the status window or on the side of the HUD while Hero of the village is active.

I've returned to my trading hall and had raids begin even though no status is indicated. I need to drink milk every time as a precaution because there is no way to tell if the status is active

While using the raid farm a new raid will begin even immediately after, even if no bad omen status is shown because I have killed a pillager captain while in an active raid.