What matters is the vertical deflection that the floor will experience. For stone, the maximum allowed deflection is 1/720 of the joist span, half of what's allowed for ceramic tile (1/360). I think you need to look at the expected floor deflections and I would do any calculations with a 50 psf floor loading (live + dead load) as a minimum. That sub-5/8" plywood is pretty skimpy, too, and I would definitely be beefing that up (plywood w/polyurethane construction adhesive, screwed down, etc.).

What is your joist size, spacing and span?

Your large format tile exacerbates any deflection issue as small tile can accept more floor deflection than larger tile. Look at it this way, place a 16" tile spanning from joist to joist and all the deflection in that sub-5/8"plywood would be experienced by the tile above as well. (Smaller tile would only bear a portion of the deflection, not all of it.) What happens when you try to bend tile? It breaks. Similar would happen with deflections along the joist length.

https://tiledoctor.com/deflection/

https://www.bc.com/wp-content/uploads/2019/06/GE-6-Tile-Floors.pdf#:~:text=The%20Tile%20Council%20of%20America,than%2014'%2D0%E2%80%9D.

See Schluter DITRA-HEAT Installation Handbook beginning on page 4.