LED instead of halogen spot

...so there could be technical problems installing 220V spotlights without a transformer there (and with the sockets shown)?

Hm, I don't see any technical defect there. I have over 80 spots with 230 V LED bulbs in my house. My wall lamps, staircase lighting, and outdoor lighting are also LED and without a transformer.

On the topic: GU5.3 are usually for sockets for 12V bulbs. GU10 are usually for 230V bulbs. You cannot use the depicted sockets for 230V bulbs.

Both the GU5.3 and the GU10 bulbs are available with MR16 reflector (50 mm housing) and are possibly interchangeable. The GU5.3 also comes with MR11 reflector, which is a bit smaller (35 mm housing).

I would do it like this: remove the transformer – clamp a GU10 socket onto the cable (99 cents on Amazonas), insert a 230V LED bulb there (e.g. LEDON). If you previously had 50 mm halogen spotlights, the LED bulbs fit into the old sockets.

230V Volt LEDs in e14 e27 GU10 etc. are rather a crutch to satisfy the mass market...

I somewhat agree here. GU10 LED is just "cheap" and more for the retrofit area. But there are a few quite decent housings that look discreet. Without glitter, without swivel range, then it's alright.

Splitting hairs.

So if real objections are dismissed here as splitting hairs, I will probably limit myself again in the future to marking bankers who can't add and the like...

What would be the official solution? Installing low-voltage LEDs with a transformer?

I would do it like this: Remove the transformer - clamp a GU10 socket (99 cents on Amazon) onto the cable, insert a 230V LED bulb (e.g. LEDON) there. If you previously had 50 mm halogen spotlights, the LED bulbs fit into the old sockets.

So simply connect the new GU10 socket to the cables from the ceiling with a terminal block and attach the LED?