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 ...
It's an excellent solution if you have a TV that doesn't support AirPlay and want to avoid using cables. How To Mirror Your iPhone To A TV Using An HDMI Adapter You can also mirror your iPhone ...
But for iPhone versions 5 to 14, Lightning is the port you need a cable for. If you still have a charger with a USB-A port, consider upgrading to a USB-C charger as iPhone fast-charging only works ...