Kitchen - gentle renovation or new kitchen?

Yes, without wall cabinets in the back would also be an interesting (affordable) option. Instead, a few simple floating shelves.. I'm back to wood there.

I would take a front to the carpenter and ask if it is possible to close the holes and paint it.

Replace the niche backs, a new induction cooktop and a new, invisible hood. For this, the carpenter can build a suitable cabinet. Nobilia and co are not a quality comparison to this kitchen.

He is bothered by the handles and the color of the fronts... what is a new floor supposed to change?

I think the kitchen would look completely different if there were a completely different floor. At least it would be a first attempt, especially if the floor perhaps doesn't really appeal anymore anyway.
A color appears different with a changed background like, for example, a picture on the wall or something similar.
Everyone experiences that differently, and in that respect, it would be an idea that I would also consider and that can be easily simulated to better imagine it.
Ideas to change handles, get a new kitchen, paint the fronts have already been there; this idea doesn't hurt, and if it's not an option, then it simply isn't.

However, it is also quite an expensive attempt if you cannot chip out and relay the tiles yourself.

As I wrote, I was thinking more about putting something "thin" on it. That was an idea for the questioner, so we both don't have to pick it apart further. When brainstorming, one should generally not extinguish the light too quickly just because they don't like it or can't imagine it. We neither know the taste nor anything else of the questioner, whether something fits or not can be decided by them; besides, an idea does not hurt.