Floor coating peeled off

As a normal part of living anywhere, I’ve been dropping food or drinks on my fake-wood floor from time to time, and cleaning it immediately with flooring-approved cleaners, but it seems no matter what I drop, the coating is completely shitty and will peel off right away (image in the first comment). Applying floor wax doesn’t seem to fill the gaps, and I find it absolutely hideous because now the floor looks always dirty. Since I fear my landlord will try to (over)charge me to fix it either now or when I leave the apartment, I’m trying to find solutions to fix it myself or at least hire someone to fix it for me without telling them, but honestly I don’t know if I have any such options. Do you have any ideas?