A transformer unknown to me in the kitchen

The connection cable on the transformer will definitely only have 2 wires since it is double insulated. You don't need more in this case.

Doesn't seem to me like you have much experience with electricity. Wouldn't you rather get some help? It would be worth the effort for me to get the cables out from behind the cabinet than to patch something up there.

I am also in favor of having certain work done by a professional, but replacing the transformer with an LED driver here will not be a problem.

Or you save yourself the transformer and simply use 230V LEDs.

The cables that were previously used for 12 V halogen should then also be suitable for 230 V. It may be, but it does not necessarily have to be so.

The cables that were previously used for 12V halogen should then also be suitable for 230V.
That may be the case, but it does not necessarily have to be so.

That is indeed a valid point.