What constitutes a change? Formatting change (making something italic)? Moving an object on the page? Or just text change? Image changes? Changing a comma to a period? Do you need some indication of what the change is?

There is an “align toward spine” and “align away from spine” feature (paragraph formatting). You can use that to your advantage by moving whole blocks, but you have to be kind of sneaky about it:
https://creativepro.com/aligning-tables-away-or-towards-the-spine.php
and
https://creativepro.com/making-an-object-or-text-change-based-on-left-or-right-page.php

Does the grep actually work in InDesign? I think it does.

It’s a fascinating question.
I’m not a copyeditor, but I think Acrobat’s annotations features cover most of the options already.
I see we had an article here:

10 Essential Tips for PDF Comments

and

Acrobat How-to: Traditional Proofreading in PDF

and

Acrobat Tips: Commenting on PDF Comments

Sorry, I don’t think I’ve seen a script or technique that would do that. It’s a great idea, though! It would be very possible with a simple script, I think.

It’s kind of similar (but totally different) than this: https://creativepro.com/topic/printing-an-image-on-a-books-page-edges

We have a number of articles on this topic, such as:
and
https://creativepro.com/import-word-files-into-indesign-remove-local-formatting-but-keep-italics-and-bold.php
and
https://creativepro.com/clear-text-overrides-from-word-files.php
and a video here:
https://creativepro.com/mapping-word-styles-indesign-styles-free-video.php

also, this post currently has a problem with the images, but we’re fixing it:
https://creativepro.com/strip-the-crud-from-word-files-before-you-map-styles.php

I also strongly recommend Anne-Marie’s excellent “Using InDesign and Word Together” course at lynda.com.