When you click on the video record button you will only record what the camera is seeing, nothing I know of can add telemetry data.
Don't know if this is something you might be referring to but it is pretty cool.
I use a I-Phone 8 plus, prior to taking off a screen recording function can be activated that records all video that is on the screen. I will usually start the screen recorder, then, after take off start the camera video recording.
The screen recording shows all information that is displayed on the screen, meaning all telemetry, camera setting and changes screens made during flight. A complete video record of the flight. Audio can also be activated, will record audio of what is in range of the phone.
Bottom line, after the flight you have two video recordings Camera, and cell phone that shows all information.
Phone video is saved and can be found in photos.
Don't know if android phones have this functionality or not.
Regards