As someone with a lot of experience in working on a Chrome extension that interacts with Gmail specifically, there are two reasons I'd expect an extension like OP's to integrate with the official Gmail API instead of poking the Gmail web app's internal API directly: 1) the official Gmail API is stable, documented, and doesn't take reverse-engineering to use, and 2) the Gmail web app's internal API is pretty strongly rate-limited for some actions.
If an extension only does actions involving the UI and data visible on screen within the Gmail webpage at a regular user pace, then I wouldn't expect it to strictly need the official Gmail API much. But this would mean the extension can't operate on emails that aren't on the current visible page, etc.
If an extension only does actions involving the UI and data visible on screen within the Gmail webpage at a regular user pace, then I wouldn't expect it to strictly need the official Gmail API much. But this would mean the extension can't operate on emails that aren't on the current visible page, etc.