i had the same issue few weeks back when i upgraded to iphone 15. I had trouble casting videos from facebook app to smart tv. I googled a lot to resolve the issue but to no avail. Cast icon was not appearing eventhough access to local network is granted to the fb app.
but luckily, i was able to address the issue purely by chance. What i did was i connected a blutooth headset to the phone and played video from fb app in fullscreen mode, this will enable the cast icon. Click the cast icon and the app will show note permission on casting requirements. Click ok or continue then you should good to go…
hope this helps, thanks