Is a TAE socket no longer needed?

What is the point of still hanging around this unnecessary can today?

Legally, Telekom does not consider it unnecessary and installs it.

So my APL was not sealed or anything. So why should I leave it hanging, who does it bother, and what is the technical difference?

In case of a fault, fiddling during the line test is counterproductive. Defined handover points help with that. But if the builder provides a proper Western socket right next to the ApL, it is said to have happened that the telecom technician gladly takes it and does not insist on installing their own TAE.

In 2017, the telecom technician sub (whom the local network operator commissioned after we wanted DSL here) labeled the existing TAE in the existing place with a cryptic sticker and recorded this socket number in the telecom technician's system. What a fuss

I have to ask something else now... I still know how to connect with the good old TAE socket and router, but if you now install such Cat sockets in other rooms, where do the cables go or how does the connection work then? They have to somehow reach the Fritzbox, right? Please explain a bit more detailed and simply.

I don't really understand your question. For the home network LAN, a star topology is usually implemented from each room to the connection room, where the DSL socket (the router) is also located.