Why do I see Telegram and Facebook but no YouTube?

Because you are on the “External communities” screen (Settings, “Organizer tools”, “External communities”): it lists only Telegram groups and channels and Facebook Pages where your games are announced. YouTube is connected in another place: open Settings (gear icon on your profile), “Connected Apps”, YouTube, tap “Connect” and sign in with the Google account that owns the channel.

Connected Apps works the same in the Playbox app, in a browser and inside the Telegram Mini App.