Try the phone and television in order
Play a single known item on the mobile device before changing any television setting. Note whether the player accepts a playlist, separate sign-in fields or its own account. Check audio and captions on the device, then try the app's supported casting or AirPlay route. A successful local playback test does not identify which external playback modes the app exposes.
What to record when it fails
Save the model, iOS or iPadOS version, app publisher and whether the failure appears before playback, while switching output or after playback begins. If casting is the failing step, repeat with a known compatible item before replacing the subscription.