The text says what is says, but it doesn't say what you wrote.
Most people will not bother to translate the French. And as you see the person who wrote below you was ready to trash his floor! lol.
The OP has dents in the floor for high heel shoes. That is not the same as worn out varnish. And much more difficult to get out.
But thanks for mentioning the "normal wear & tear" issue. It's an important one that often gets missed. And I agree the OP needs to push back.
We`ve been in and out of rented apartments, and usually they allow us to accompany them armed with our cleaning stuff for things the "normal" eye missed.
But a stove top! You cook on it minimum 3 times a day! Pots are heavy things, of course it will get a few scratches!
The last flat we left, the vegetable drawer was cracked, and the grid in oven was rusty .... the owner agreed both needed replacement, as normal wear and tear.
The only fall-down we had .... I had tried to wipe off the fly-shite from the lounge ceiling, and in the snow-white reflection of a snowy sunshine afternoon the white spots showed, so we were allowed to repaint the ceiling. Then the new tenant complained that the rest of the flat had "not white" ceilings ...... and she was told to accept it!
Leaving the fly-shite, we were told, was a better option ..... "natural wear and tear" as flies are part of life and living.
Oh come on! even deep scratches on a stove top are normal wear and tear unless someone took a diamond and deliberately dug into it.
How does that happen? The floor has got to be soft or the shoe-wearer has got to be heavy, or striking the floor with force.
I wonder if dropping a loaf of week-old bread would leave a dent on that floor.