You wouldn’t even really question your new device on the network. Since the monitor must forward the packets from and to your PC it’s MAC address would show up in the network, but that’s expected. And good luck separating the traffic of your monitor from that of your PC if it originates from the very same MAC address as it’s basically the new network card of your PC connected via USB C. And since it could act like a bridge, it could strip out the responses to its own requests and not forward those to your PC so you don’t even see them there. On the other side it’s all TLS encrypted so nothing to see either. Heck, it could even only send its own requests when your PC is actively using the connection so that it’s less noticeable.

You might do some DPI and check what IPs you connect to but good luck finding if it really is your monitor and not some random app on your PC. If it’s using DoH, you can’t even inspect its DNS traffic to get a clue what’s going on (SNI in the handshake might still offer some clue).

Also all of the above enables tracking and spying on you covertly. Ads are quite obvious, so there’s nothing to hide there.