When your doorbell, vacuum, fridge, tv, mouse, computer, security system, nanny cam, all collect and sell data about you why would you not assume that your monitor (likely now connected by a shared data channel like usb3) is doing the same.
Hell, MS went as far as to say capturing regular screenshots of your activity was a feature. It won't be long before most people agree with them.
When I was young, people feared that the powers that be might be listening in on their phone calls or watching them through their TVs. Today unfortunately, most people consider these to be product features.
You can easily verify by simply logging all data in/out of your network that the monitor is connected to and seeing if there is any unexpected traffic etc.
Some manufacturers are known to have added backdoors or methods to access data on remote devices but the internet community love tearing things apart, dumping firmware etc to see how things work and someone ends finding it in the end.
Not that it's the correct way of thinking, but if you have anything actually worth capturing in that respect and you believe you're being watched, you'd need to findn alternative ways to access it.
Its difficult to escape, tho. Everything that receives RF, also transmits.
If you air gap everything and live in a Faraday cage, they'll know for sure that you have something to hide.
If that proved to be true then OP isn't being paranoid, they're being prudent.
I'd hope that it's not true.