Oh, man. That’s a tough one. Because the text boxes are comments in the PDF, they, as you have discovered, will not be in the PDF when you open it in Illustrator. But you can use a Flattener script (on your PDF in Acrobat) that will flatten your comments so they’ll no longer be comments, but rather, part of the main body of the PDF. Then when you open the file in Illustrator, they will be there. But, since you’ve opened PDFs in Illustrator before, you’re likely familiar with the fact that Illustrator often breaks up the text into bits and pieces, making it much more difficult to edit.
Is there a particular reason you need to add the callouts in InDesign? Because Illustrator also has paragraph styles and may be a better choice for this project.
Regarding the content of the comments, there is way to export all of them out as an FDF file. That’s basically a type of XML file. I wrote about that here: https://creativepro.com/working-with-fdfs-forms-data-files/
A scripter can probably write a script that will extract just the information you need (the contents of the text boxes), and get rid of all the other stuff. Just two days I saw that type of script in action. Once all your text is extracted, it would be fairly straightforward to go in and apply the styles you need. Here is the contact information of the scripture was can help you: https://frameautomation.com/about/
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