How much can my phone influence the circuits of the desktop screen?
The phone contains an RF transmitter for communicating with the cellular network. If the closest "basestation" of cellular network is far away or there is a lot of interference, then your phone will transmit at higher power in order to compensate for that.
The phone maintains a wireless connection to the cellular network so periodically it has to let the network know it is still ready to receive a call. For that it needs to transmit signals to the cellular network. Those transmitted signals can also be picked up by other equipment. The most common phenomenon I have experienced is when radios and (PC) speakers start to make click-bzz sounds when the phone is transmitting.
Depending on the design of your monitor, that monitor could be disturbed such that it thinks there's no signal present or that it needs to switch inputs. That can happen if the electronics in the monitor aren't shielded well enough.
Generally monitors aren't designed to not be disturbed by a phone transmitting at maximum power closeby. I see it as "bad luck" that your monitor is sensitive in this respect. A different monitor could respond differently or not at all.
Would it be possible that changing carriers has something to do with it?
Yes, the carrier could use a different frequency band which could work better or worse in your situation. It can also be that a different carrier has a basestation that is closer to your location and then your phone can transmit at a lower power but still keep the connection.
Possible solutions are:
- placing the phone further away from other equipment
- changing the type of network connection, maybe you're using 2G (GSM) but 3G or 4G (LTE) could also be available. Most phones have a setting for this so try that. It depends on the phone and the cellular network what is supported and what is not.
- not preffered but I mention it anyway: shield the sensitive equipment by using tinfoil of copper foil or any other electrically conductive material.