At present my master socket is in my living room, in an awkward position. A couple years ago I had my house cabled with Cat6 with the termination point being the garage where the patch panel and network switch are. Whilst doing this, the installer ran what looks like Cat5 or Cat6 from my master socket into the garage too.How is the master socket fed, for a starter! The OP says the termination is in the garage, where there is a patch panel and a network switch. Plus an unterminated wire he thinks is from the master ending up back in the garage.
I now wish to take advantage of this and move my BT Openreach modem and Asus router into the garage. My knowledge of BT faceplates and sockets isn't great. I've unscrewed the master socket and from the top of my head, terminals 2 and 5 have been punched in and are going into the garage. In the garage, the other end of the cable is waiting to be wired into a socket.
That simply does not make sense unless the patch panel and switch are not in use. In particular not connected to the master.
If either of them is feeding the master then the termination is indeed in the garage and the wiring is all wrong. Classic star wiring.
If neither is, i.e. they are not in use and the termination is still on the A/B terminals of the master, then the feedback to the garage needs to me from the auxiliary A/B terminals of the recommended new master faceplate not 2/5, assuming that particular one has such, and connect to 2/5 or whatever the appropriate terminals on the suggested extension are, as it seems to be a dual socket extension with further auxiliary A/B connectors.
I assume the router will feed the network switch. (It's decades since I used to set up modem <> router <> switch configurations so I may have that part a bit confused). Which makes me wonder how any extensions are currently supplied unless all are on wifi from the router.
I also wonder if we are talking about a boarding house/small hotel.
Have I developed brain-fade somewhere when reading the OP?
Thinks - maybe. Perhaps the current master is fed normally, direct from the incoming line and not through the garage. In other words the garage is the termination for the CAT6 network, not the incoming line. In which case we will still have a mess as the suggested filtered faceplate master socket will output VDSL2 + PSTN into the sitting room from the VDSL2 socket. Not ethernet from the router.