When cats have a UTI, it is painful to pee and that pain is often associated with the litter box, cuz the last time they peed in the box it hurt, so they find somewhere that is softer to stand ie a rug, the bed etc thinking it won't hurt cuz they're not in the box but it still does, plus it's more comfortable to stand on that soft spot while trying to pee.
I would bring her in for a cystocentesis to get a sterile (
) urine sample so they can check not only for crystals but also bacteria, if that checks out fine then it's onto other possiblities