oooh that doesn't look yummy at all... If it were me, I would tear it all out until you get to the smooth concrete below. Best bet is to go to a tool rental shop and see if they have a 6" hand scraper. Remove it all so that if you plan to glue anything else down that it doesn't come back up down the road.

Sometimes you can find longer scrapers that will save your back.

Have a piece of that bottom flooring tested for asbestos and also the adhesive. The peel and stick may have been a cover up for the original tile because of asbestos either in the tile itself or the adhesive.

The black spot doesn't look like mold it looks like some kind of tar like residue. The peel and stick tiles don't look to be old, like from the 70's or older, they look fairly newish. I don't think the even made peel and stick tiles when asbestos tiles were used. The old style asbestos tiles were glued down glued down.

But maybe wrong.https://inspectapedia.com/hazmat/Asbestos_Peel_Stick_Floor.php

I just noticed the second layer of vinyl and what looks like a the black tar like adhesive that was used on older tile. Yeah, maybe check for asbestos on older tile and adhesive too.

Peel and stick, do not have asbestos, but there is a good chance the layer on the floor does.

That black adhesive could be asbestos-containing "cutback." I don't know that I'm convinced it's worth having it tested, but that's up to you.

I've safely removed old cutback on concrete with Bean-e-doo. It's messy, but not difficult. You need more than the label says; I did an area roughly 10' by 25' and 5 gallons was barely enough. It has to soak longer than it claims, too. I'd leave it on for a week or so if possible.

Bean-e-doo is a bit expensive, but it's approved for removing asbestos-containing adhesive. As far as I can tell, it's just soybean oil. Generic soybean oil is not an approved product for that purpose, but it usually costs a lot less, wink wink nudge nudge.

We had this same issue in our previous house. Used a heat gun to loosen the old adhesive, and then a scraper like the one pictured above to remove the bottom layer of tile. An old iron worked well also. DH used the heat gun, I used the iron to loosen the glue. It took us a week (2-3 hrs each night) to get it all down to the concrete.