Dear Dr. Kessel, dear all,
thank you for this helpful hint. May I add some further information:
(1) The software most likely working in the background of google docs here is tesseract, developed by google, too. It is open source, though (more information here: https://en.wikipedia.org/wiki/Tesseract_(software)). The documentation on the usage and trials for Arabic has been steadily growing, while I cannot find anything on Syriac.
(2) There is a tool to crop multipage pdf files, which might come
in handy to process the text and the footnotes separately, at
least if the pages have a more or less similar layout: https://sourceforge.net/p/briss/wiki/Home/
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