I was having issues with multilingual keyboard after the update, and a restart fixed the issue. You should try to restart your phone to see if it fixes it for you.
AirPlay uses a few protocols that can single out a device and leave others working. Restart the AppleTV, iPhone and the router. Are you using a VPN? If so try disabling it temporarily to remove variables.
I admin a few hundred iDevices and Macs for a school - on some devices iOS/iPadOS 18.4 had access right problems (leading to airplay or casting problems) which disappeared after shutting the devices down and powering them up again (a simple restart did not help).