Bleach removes the color or pigment. I do not think you can remove bleach stains. You may have to mask the bleached spot with a marker or sharpie of some sort.

Depending on how uneven the stone is in other places, you might be able to chip out the part that you don't like and then seal the newly exposed surface. I would ask a professional though, before even attempting to do this. It could easily make things worse.

A stone floor can be ground down and resealed. This is something you can look into. Feel free to reach out to a stone refinishing professional (anyone who lays marble or slate) and get them in there to do a deep clean. Let's figure out how much needs to be done to these stones before grabbing your chisel.

Once the stones have had their deep cleaning (and the mortar/grout lines) you can then reassess. If they need grinding/polishing, then go ahead and have that done. That's the beauty of these long-wearing floors. They can be refinished and refreshed for decades. They should out last several homeowners.