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.