screen annotator & recorder

Annotation being by definition involving some kind of editing of text content, just to clarify are you asking for an app or service that does OCR (Optical Character Recognition)?

If you want to capture the text on a screen, and accuracy is the priority, you'll be better off just doing a copy and paste of the text itself. That will result in an exact copy from one to the other. (i.e. copy the text you want to edit and then paste it into a text editor or word processor to do the actual annotating.)
OCR on PCs is pretty advanced these days, on phones they're catching up but it's still matter of taking an image of the screen, applying software solutions to scan, interpret, and then convert that converted image content into text.

 

Is this a matter of taking a screen capture, which results in a photographic image? Your device will have that capability. What phone do you have and which version of Android is it running?

Or do you want to record your screen in real-time, which results in a video file? There are a lot of third-party screen recorder apps or if your device is running Android 10, you might already have that ability:
https://android.gadgethacks.com/how-to/enable-built-screen-recorder-android-10-0194955/

 

Perhaps one of these apps might be suitable,
https://blogs.systweak.com/best-screen-recorder-apps-for-android/
but hopefully someone with actual experience with a good 'video with audio' screen recording app will be able to make a more helpful suggestion.

 

You may wanna have this app..