Isn’t their a Mapai artic white? I think I used that and my tile is similar to yours

The way you analyze a floor finish: view it from a standing position (not up close) from 10 ft away (yep...10 ft) in NATURAL lighting. That means you will probably need to view the tiles from outside the bathroom. IF you can STILL SEE the scratches from that distance and from a STANDING POSITION then you have an issue. If you cannot then there is nothing going on. Nothing wrong. And that's not 'semi-polished', that's full gloss!

Windex is your friend. Windex original formula (with ammonia) is a lovely degreaser. The 5% ammonia content is IDENTICAL to 'commercial' floor strippers. If it can clean windows and mirrors it does VERY well with shiny tiles. And yes...the HIGH GLOSS finishes are SUPER TOUGH to live with. They show EVERYTHING. The super matte floors ALSO have these issues. The EXTREMES are hard to deal with (should come with live-in cleaning people). The biggest thing to remember: water evaporates but DIRT and MUD do not. If you want to remove the dirt you need to TOWEL IT OFF. If you use a damp mop, then you MUST towel dry the water off the floor. The towel picks up the mud as well as the water. And...of course, start wearing slippers. The oils on your socks = skin oils. They drop oil. Oil GRABS dust. Dust lines the foot print and makes it visible. I would personally look at purchasing a gallon of Windex. Use it FIRST. Then try the steam mop. NO OIL-BASED soaps or cleaners. Anything that says 'Eco-Cleaner' is GUARANTEED to be an oil based cleaner...."Natural Orange oil", "Thyme Oil", "Sage Oil", etc. Get the idea? All of these oils will SIT on your floor. Again, water evaporates but OIL does not.

We are in midst of planning for 4 showers in a new build and I am very focused on the tile floors not being slippery-- many years ago, one of my kids slipped on regular ceramic tile and slammed her foot into the wall, breaking it. I keep hearing that the grout lines will solve the risk (designer likes polished carrera marble) but I have been looking at honed but not polished tiles for that reason.