120x120 tile / piece broken

Aha. Interesting point of view. I’ll get a floor layer, drop a hammer before acceptance, and then say: "Your problem, craftsman!" The craftsman is right here. If other companies are coming and going in the house and no one wants to take responsibility, then it is the client’s problem. So glue and grout.

quite honestly,

Quite honestly? In overview picture 3 you can hardly see anything.
Once it is grouted, only a few millimeters remain.
( probably some cement paste is enough for that one corner ;))

Each trade must protect its work until acceptance so that it cannot be damaged during the normal construction process. This does not exempt the party responsible from liability for damages, but if it cannot be proven... However, this specific requirement will hardly be enforceable. Therefore, it is better to focus on cosmetic repairs.

I find the outline for such a ministelle unjustified. And it is obviously not even grouted yet and already you practically need a magnifying glass to see a problem there. This can be repaired with minimal effort.

The craftsman is right here. If other companies are coming and going in the house and no one wants to take responsibility, then that is the client's problem.

How do you come to that narrow conclusion? The magic word is transfer of risk. This must be documented in writing. In case of doubt, it must take place in several steps if the contractor cannot secure his work.

Normally, another craftsman drops something, for example, a hammer that damages the tile. He sees the damage, goes to the client, and his business liability insurance covers the damage. That's how it should be.

The craftsman might not even have business liability insurance and conceals the damage. No one saw it. It wasn't the tiler. Therefore, there is no damage causer who can be held liable for it.

We know it from traffic accidents, this is called hit and run. The tiler doesn't care. He doesn't know who the culprit was or who else is working in the house.

One must also say, if the tiles had already been grouted, this damage probably (hypothesis) would not have occurred. The tile edge was hollow and broke off.

The damage can be repaired without much fuss. The tiler will surely need 3-4 hours to replace the tile plus the risk of further damage to other tiles. He wants to be paid for this risk.

There are 3 options for the client. Repair it yourself, pay for repair by the tiler, or find out who caused the damage.