How flat if the tile floor currently? Vinyl needs to be 1/8" within 10' in flatness. All the grout joints need to be filled in for vinyl or they will all telegraph thru in short order.

i think the LVP is a really good option for a basement. Tile is cold and hard.

Millwork has good advise. Just to your research when you decided which vinyl product you use.

The tiles are pretty well laid except in one room where there’s a hump. If we go with vinyl we are planning to seal the tile grout before putting down the vinyl.

Not seal it. Fill. In. Every. Joint. with thinset.