Personally I run the cables up into the attic/loft and then back into the rooms. Luckily the previous owner already had TV antenna run to each room, so the holes are already there. The other option I’ve used is to follow the central heating pipes, although this only works for me as I’m using industrial cable that’s okay with the heat.
Failing that you could use power line adapters but these aren’t the best.
Other than mounting the switch above and running the network cables up the rear there doesn’t seem to be a easy solution