It's really a matter of how well the adhered tiles are stuck. If you can get something like one of those roofing tear up bars underneath and pop the tiles up in full pieces, you aren't likely to generate much asbestos dust. The adhesive can have asbestos also so it could be wet scraped and picked up with a wet vac with a capture bag. If the tiles are adhered such that they break into little pieces, you can likely float where the loose tiles came up and put a new floor over the top. There's also floating vinyl floors that sound like an ideal solution for your situation but I know little about the efficacy or quality of these products.

With lots of expensive prepwork, and undercutting all the casings and doors, and losing height of the baseboards, yes, you can halfass the project and lay plastic over tile. It won’t be any cheaper than doing the project correctly and removing the tile. It’s likely to be more expensive, actually.

tile and vinyl plank installation

The tiles will hold up better, but are colder and harder. The tiles are best for wet/humid rooms. I think they are more attractive. Also easier to keep clean. But they are more expensive than LVP to buy and install.