iPhone as webcam for the Mac (continuity camera)

So, I'm trying to use my iPhone 13 pro as a continuity camera for my Macbook Pro (2021) but I can't get it to work. Specifically, I want to use it as a webcam to take calls or record myself.

I've tried everything. Bluetooth is on, Wifi is the same. Continuity camera and Handoff are activated.

I can perfectly copy and paste things between devices and send pictures through Airplay. So systems seem linked through iCloud.

Software is up to date on both devices (iOS 16 and Monterrey 12.6). I've tried resetting network settings and rebooting but I can't get it to work. The camera just never shows as an option in Photobooth/Facetime/Quicktime or any software that uses cameras.

Any ideas? Thanks!