I would guess that those yellow marks are from rubber backed rugs. It is my understanding that they actually cause a chemical reaction and can't be removed. It is a known problem with vinyl flooring.

If it’s a linoleum rather than vinyl you can sand it and reseal it with a good wax. Linoleum color goes all the way through, vinyl is just on the surface.

Without knowing what the flooring is it is next to impossible to offer much in the way of removal advice. It is possible if that is linoleum or vinyl it is never coming out.

1995 circa vinyl is done with. Replace it.

Looks like there was a rug, or something else sitting there. A cat littler box, maybe. I have a similar place in an area of white vinyl, where I have a dog crate. It is caused from the dog crate sitting there. It does not come off, its there forever.

It's not done and needs no replacement. These upper end Solarian floors can last 30 years or more. They usually get replaced well before they're truly done.

I'd have a rotation of nice areas rugs since these stains usually happen where people stand a lot. A proper mat would have avoided it and will stop it from getting worse, or everyone can swap shoes at the door.

Sometimes these traffic areas get tiny scratches that fill with soil. Take a Magic Eraser wetted with mineral spirits and scrub one square or strip. Use proper precautions.

You might try a steam cleaner and/or hydrogen peroxide paste made with baking soda to bleach the stain. Try it on a small spot first, letting it set for a while.

Try straight lemon juice and let it sit.