My thought is it’s about the look you want for the vanity. It is a floating type - to maintain the appearance of floating, the baseboard under the vanity should disappear so it should be painted the wall color. is there an obvious stop / transition point at both ends of vanity? If yes, I’d paint only the under vanity portion & see how that looks & leave the rest. You could try mocking the look up with white paper taped to baseboard.

The baseboards don't match the vanity, either. So yes, I'd paint them the same color as the walls.

Paint them to match the wall color so they blend it and don’t stand out.

Agree with KW, it should blend into the wall