TLDR: can a put a bathroom vanity in without attching the backsplash that comes with the vanity top?

Hi! I was planning on doing a refresh to our 1976ish bathroom, but upon sanding the vanity it occurred to be it could have lead paint so I tested it. Sure does! We thought about sealing it with the options available but the pint was already chipping, bubbling and peeling so everything I’ve advised says not to. We don’t want to do a full bathroom overhaul for a few years. Upon looking for a vanity, everything is too tall once we add a backsplash that comes with the vanity tops. Our current lead vanity is 50” wide x 21” deep x 31” height with the countertop on.

I can handle a standard 48” wide vanity even thought I know we won’t have tile on those two inches because I planned on putting pop tiles on the floor. The issue is the height. We have a huge mirror starting ~34.5” up the wall and we don’t want to remove it right now. I picked out a vanity but It’s too tall with the backsplsh. Can I leave the marble backsplash off and paint or simple add different tile? TIa!