I don’t think it’s a venting problem . . . the drain pump vents directly into the building’s vent, and there’s no evidence of any odors anywhere else but in those two basement sinks.
from your post you say (Vanity), but you are not installing a vanity.
very misleading.
REgarding the vent, check to see if the sink trap is still full of water after the sink drains. A clogged vent can cause the traps to be “sucked” dry, letting sewer gas back into the building