How to automatically pull text out of a video
I do not know of any existing solutions for this in Premiere or AE.

However, if you know a little about programming, you might be able to write a script using OpenCV that runs Tesseract OCR on video frames, and comes out with the text you want. Once you have the text and time codes, you definitely could write a script to build the titles at the appropriate time codes inside of AE or Premiere.

(I became aware of these open-source tools since I am currently building a mobile app that runs OCR on documents.)

Check out the Scene Text Recognition docs for OpenCV, if you want to try that route.