Not for handwritten text, but for printed fonts, getting OCR is as easy as just making a box in screen with current technology. So I don’t think we need AI things for that.
Personally I use tesseract. I have a simple bash script that when run let’s me select a rectangle in screen, save that image and run OCR in a temp folder and copy that text to clipboard. Done.
Edit: for extra flavor you can also use notify-send to send that text over a notification so you know what the OCR produced without having to paste it.