Assuming the floor is flat and the adhesive is non-asbestos, the easiest, quickest thing to do would be to scrape the adhesive down to a thin film, removing as much as possible and sprinkling portland cement floor patch over the thin film of adhesive(wear a dust mask) and vacuum up the excess. This will neutralize the tackiness and allow you to put down your vape barrier and cork underlay without annoying sticky sounds.

If it is black, I would encapsulate it, possible asbestos, or at least have it tested. Otherwise, a multitool with a scraper blade would do the trick.

No, it's white. We've spent a lot of time on hands and knees scraping at it already, it sounds like we need to go back to that. Yuck!