I wonder if you aren’t just hearing it because you aren’t playing music. :)
I don’t have a dedicated line, but I have a separate line to the stereo but the ceiling fan noises sometimes still comes through, even when it’s being turned off in another room.
I am curious that the TV is affecting you however, those tend to be relatively low power devices so hard to imagine it causing as much AC noise as a motor. Perhaps as another has mentioned, this is an EM induced coupling with your dedicated line caused by the wires getting too close.
It could also be unavoidable. The house panel is just not a perfect AC reference that many think it is. Internal surges can cause voltage spikes across the entire home due to resistance/inductance in the wiring from outside transformer to the home. A very fast spike on another circuit can elevate the AC at the panel which takes a few milliseconds to clear. A perfect, dedicated line to the panel will just help to transmit that to your gear. In this case, a little R and a little L on the circuit to your gear can actually be good.
Check your neutral to ground and make sure it’s 2V or less when your gear is on. Any higher and you may have a loose neutral. If you are going to get into your panel, check that your neutral wires don’t share a screw and are tight AFTER you turn off the main panel breaker.