Cooker connection not via RCD/FI although available - is rewiring advisable?

Now it’s not just the stove but the whole kitchen?

Well, the usual stuff that belongs in a kitchen ;) Unfortunately, besides the stove connection outlet, there are only two sockets at countertop height, each protected with 1x16A. So everything has to run through the stove connection... And that’s also why separate oven and 2-burner hob. I just don’t want to tinker, that’s why I’m asking here. I can understand the existing 2x16A per phase – the residential unit is protected with 75A in the main panel. So I’d have to give the stove connection outlet its own RCD or replace the existing one?

Please draw where the supply line is and where the stove branches off. Top left the 3 LS supply line or does it go to the stove there?

Sure, gladly, see attachment. Is that clear?

Ok, that sucks. This is how you (I) can misinterpret a picture, thought the supply line and the stove were reversed. is absolutely right: Get someone to do it properly for you. It's not just 3 wires you have to switch to fix this.

Thanks for watching. Could you give me a little push so that I can learn something too?

I would have expected that if I put the three phases "behind" the RCD, it would work properly for the first time, of course with the limitation that the RCD can only switch 3x40A and therefore should urgently be replaced by a 63A one. Or am I thinking about this wrong?

At the manufacturer of your circuit breakers (among others), you can find the information that the maximum rated current of the circuit breakers (per phase after the RCD) must not exceed the rated current per phase of the residual current device (this is what RotorMotor meant). Alternatively, a fuse can be used whose rated current is less than or equal to the rated current of the respective RCD (this is what I meant, due to a misinterpretation of the picture).

Your electrician whom you will hire for this can either use an RCD with a higher rated current or back it up with a 3-phase circuit breaker. He could also connect the stove supply lines to the existing circuit breakers in such a way that neither is necessary. However, then you cannot operate everything simultaneously at maximum load.