Allways epoxy for me ...I know a few tilers now who will just do the grouting for customers where their so called tiler has refused to use it?? Kerakoll fugalite and Mapei kerapoxy design I find lovely to use
Silicon movement joints are ok short term but look grubby after six months ...I would use Schluter’s perimeter and intermediate profiles. ..many colours and does not deteriorate like Silicon making you install look better for longer.
Looks like a poor job... from the picture of the removed tile it looks like the old tiles were removed and the old adhesive has just had the high points removed....I would have used levelling compound be fore tiling to get a better floor.
Sort out floor boards first and then overboard with 6mm No more ply if you plan to tile it.... also are they going to tank the walls before tiling?....they should.