The entire shower needs to be finished being demolished. And only then do you start building it back. You cannot do "just" the floor" as it must integrate into the wall waterproofing.

Use a wide chisel and hammer and chip away. I myself would use a rotor hammer with a wide chisel to clean it off but I'd only take off the groves then float the thin set over the top with new groves. Make sure you butter the back of the new tile with your tile adhesive before laying them down.

If the water barrier wasn't breached you can lay the new floor tile without tearing out everything. Usually doing the floor first before the walls will allow you to cover the floor tile edges for a cleaner look, but it's not a problem doing the floor last as you're doing and will NOT cause an issue with water leakage if you didn't wreak the floor pan.

" You cannot do "just" the floor" as it must integrate into the wall waterproofing."

You certainly can according to the Tile Council of North America. No need to demolish anything; tile over tile.

https://tcnatile.com/resource-center/faq/existing-ceramic-tile/