It depends on the playback method and app. A dedicated supported video handoff can behave differently from screen mirroring, and background playback may be restricted. Test the exact workflow rather than assuming that locking the phone always leaves television playback running.
Identify the current method
If the television is reproducing every phone menu and rotation, you are likely mirroring the screen. Locking that screen can affect what is mirrored. If the app has handed video to a receiver, the receiver may continue independently, subject to the app’s supported behaviour.
Review device power settings carefully
A phone can restrict background activity or network use to save power. Those settings may affect the sending app, but disabling all battery controls is a broad response. Read the app and operating-system guidance and change only a relevant setting when the workflow is supported.
Keep a practical viewing plan
For regular long sessions, a native app on the television device may be more convenient where officially supported. If using a phone, keep it charged and avoid exposing private content through mirroring. End the session explicitly when you are finished.
