When connecting an iOS or iPadOS device to Reflector 4 on a Mac with macOS Sonoma you will need to disable the AirPlay Receiver setting in the Mac’s Sharing menu.
Without disabling the AirPlay Receiver setting on the Mac, your connection from the iPhone or iPad will utilize the built-in AirPlay Receiver functionality on macOS Sonoma instead of an AirPlay mirroring connection with Reflector 4. Connecting to macOS Sonoma’s AirPlay Receiver function will prevent iOS and iPadOS devices from connecting to Reflector 4 and will limit screen mirroring capabilities.
Find the AirPlay Receiver setting on Mac here: System Preferences > General > AirDrop & Handoff. You will want to ensure this setting is disabled to allow for AirPlay mirroring connections from iPhone and iPad to Reflector 4.