Hopefully others will fact-check me if I've found something incorrect. Based on my reading, and experiments with the Kobo desktop reader:
1. All highlighted text and annotations are stored in the Kobo.sqlite file.
2. The text is stored in the file (essentially) by book, so you do need to click through each book to extract the annotations. This may work differently in Calibre.
3. The annotation information isn't as extensive as the Amazon setup. You get text and no location information.
I'm not knocking either platform; Kobos have several other advantages that may outweigh the inconvenience of this for me. It's more a FYI for others considering the jump.
For others with the same question, I found some helpful threads:
How to save highlighted portions of books, which includes a link to a
stand-alone program that extracts highlights and annotations from the Kobo.sqlite file.
A
Kobo Utilities plugin for Calibre is also available, that has somewhat similar functionality among other stuff.