I know some people have had luck painting interior tile with chalk paint and there are porch paints that you could use with a good primer (talk to your paint store), however if it’s just the mortar that’s bothering you, maybe just recolor that. I can’t tell if that’s interior or exterior? It appears to be not flat or level, so in that case I would replace it.

I painted my bathroom tile floor several years ago. I'm not sure of what type of tile it was other than the ugly kind ;-) I used a solid coat of Behr wall paint, then stenciled a design with chalk paint, and I applied several coats of polyurethane along the way. That was 7 or 8 years ago and it still looks great with no chips or peeling. It was a cheap and easy project that made a huge impact. Below are photos of before, a couple of weeks after, and 8 years later. When polyurethane is applied over light colors of paint it causes the paint to yellow over time. Other than the yellowing, the floor looks the same.

Your floor looks more porous than what I was working with because so much of the area is filled with grout. That should help the paint stick. I think there are now products on the market for painting tile, though I am not 100% certain.

Rather than paint everything have you considered cleaning the stone and recoloring the grout?

Here are some before and afters with tile.

https://www.sirgrout.com/blog/can-grout-be-replaced/

I cleaned and recolored the grout in my home. Before is the listing picture.