I have been working from home for years and my employer is not watching our screen. However about a decade ago we received a company wide email from an admin reminding everyone that they can see DNS requests when we're connected to the VPN.
Sounds like he's remoting into the computer in the office from another computer at home (pretty common in IT since you probably have admin tools perfectly configured on that computer and specifically configured for its network config) but with Windows Remote Access it lets the person physically at the computer see everything by default. But i would really hope that someone in IT would be painfully aware of why you shouldn't do sensitive personal browsing on a work computer or a work network
I don't RDP that often to physical devices, but I'm pretty damn sure the default settings for RDP forcefully logs/locks out your user on the physical device and only your lock screen is visible. I have never tried it but I'm also pretty sure it's possible to have two logged in users at once, one using RDP and one using the physical device.
Remote access with continuum/connectwise, TeamViewer, etc gains access to the screen including for control but doesn't normally black out anything locally.
If its in a common area with speakers, anyone can both see and hear anything done on the machine.