You will get wear paths that are red in between the bucket of paint accident.

are your tiles porcelain or clay? hard and shiny or porous? That would make a difference in what you do. I have painted concrete in my breezeway mudroom and have had no problem with it wearing of in spots. I used and exterior paint, not even an epoxy.

I am thinking since you want it white you might want to use just a primer. That should stick well. But how you apply it is going to depend on if your tile is porous or not.

I believe you are working with quarry tiles. I don't see achieving the look in your second photo. One of the main features is the chiseled edges.

You definitely need to ascertain if these are tile or brick...paints and finishes need to penetrate to be durable...

Just as an aside we had stained concrete floors with for over 15 years...finish stayed same that long as it was a stain...in the converted garage space we used plain old spray can paint and it is also still holding up...with a spray and wipe technique on a porous surface and perhaps a smoother finish....will probably get the finish you like...maybe using white primer as it has no shine..spraying a more solid coat on the grout lines...this paint sticks like glue to almost anything ...and I always use the cheapest Walmart brand spray paint ...

I would attempt it only if I was OK with having to rip it out and replace. Because the potential for failure is huge. In all likelihood, the floors have been treated with sealers/ penetrating sealers and who knows what all else that could interfere with any subsequent products adhering to the surface.

At best, referencing what Creative Tile said, I think that even if the color washing attempt succeeds, you'll end up with a floor that looks like 'someone tried to make quarry tile look like brick'. Because quarry tile is a uniform product that doesn't have the subtle texture (pits, rough edges), color & irregular size differences that real brick has.

Maybe try it in the (small?) laundry room first before committing to the larger & more public den area?