Which light bulbs - only LED or others as well?

2020 is a switch/button, there is no question about that.

Am I correct in assuming that this is a button for you?

I suspect you have a dimmer somewhere in the circuit (or in the lamp), which then takes over the dimming function when activated.

Wie werden Halogen-Birnen kaufen: zwar verbrauchen sie mehr, aber man kann die dimmen, und der Verbrauch gleicht sich mit der Ersparnis des neuen Dimmers wieder aus.

And the light is simply more pleasant, in my opinion.

I suspect you have somewhere in the circuit

Could it be that there is a relay in the electrical cabinet that takes over the function?
Our construction lamp was dimmable too... We had ordered, paid for, and received a dimmer as a push button from the electrician back then.
I am a complete dummy when it comes to electricity...
My husband can only install lamps...

Is there a relay in the E cabinet? Like something that doesn't look like a fuse?

But since you mention it: in the bathroom we have a real rotary dimmer... for whatever reason the electrician made distinctions there :(

There is one more option. In our dimmable living room lamp, the dimming electronics are built into the lamp. That also exists.

Is there a relay in the E cabinet? Something that doesn't look like a fuse?

YES! HOW EMBARRASSING ...
My husband withheld from me, or rather he himself no longer remembered (men!),
that an acquaintance told him about a faulty part in our E cabinet and gave us a replacement part... it's actually in the E cabinet waiting to be installed, which of course my husband didn’t do himself and totally forgot about.
hm .... Nevertheless, I will now stick to the halogen issue.