the good news is that mirroring your iPhone to a TV is easier than you think. There are several ways to do this, including using Apple's AirPlay technology, HDMI adapters, and third-party apps.
The Studio Display will be supported too, obviously. Another tidbit from Apple’s support document: You can connect your iPhone to an HDMI display or TV with a USB-C to HDMI adapter or cable. Adapters ...
This is one of the easier options, but you will need to buy or acquire a specific adapter from Apple ... an extra HDMI cable ready to use, as it will be used to physically link your iPhone to ...