OK, I see what you're trying to do. I'm going to set aside the device question as it sounds like you're on Android either way, so it's a matter of choosing which device hardware you like best.
Believe it or not, what you want to do is surprisingly tricky (so this is gonna get a little lengthy :-) ). Because you actually are trying to meet several requirements with a single solution:
* Run several book-and-annotation ecosystems and their apps (Kindle, Google Books, and generic epub) on a single device.
* Find a solution that would let you (1) Take annotations in your Google Books and generic epubs, and (2) Automatically sync those to the cloud without requiring manually exporting the annotations to some other format.
* The cloud server for the syncing must be Dropbox.
There are probably new options, there's always something new. But I've checked out this issue before myself, tried different approaches, here are a couple of options I've tried. Unfortunately, some of these would involve a compromise on the Dropbox requirement for your cloud storage; still think they're worth considering. But listed a couple of Dropbox options below too.
Option 1: Use Amazon Kindle as the 'book and annotations hosting service', for ALL your ebooks. Basically, you De-DRM every book you buy, and store the original source version of the book in its native format (Epub, AZW3, etc.) in Calibre. You keep your book source files DeDRM'd, organized, tagged, and backed up in Calibre, but beyond that you don't do a ton with Calibre. To get your DeDRM'd Google epubs and other epubs into Amazon, you have a few different options. For example, one simple option is the 'send to kindle' option, where you email the DeDRM'd epub file to your specified Kindle address, and Amazon converts it, adds it to the "Personal Documents" area of your account. Once the book is in there, you can read it on Kindle, you can take notes on it, those notes sync to your Amazon account, etc.
It's actually super slick, this is what I use now, and this is after going full circle over about 10 years, trying all the other approaches . One limitation is that you can't do a lot of organizing your collections on your device, with Kindle books.
Option 2: Use Google Books as your epub-book-and-annotations-hosting service' for all non-Kindle books. So in this approach, you leave your Kindle books in your current solution. You use Calibre to DEDrm and convert all other ebook formats (besides Kindle, and your existing Google Books epub files) to epub. You upload the converted epub books to your Google Books account. You can store up to 1000 non-google epubs in your account along with your Google books, the notes will sync and work just fine. I've used this in the past, worked ok-ish, but didn't like the 1000-book limit for external ebooks. Also didn't love the Google Play ebook reader itself. These days, all I use Google Books for is BUYING an occasional book, but I immediately DeDRM, move into Calibre for storage, and put the converte file into my Kindle account as above.
Option 3: Use FBreader as your epub-book-and-annotations-hosting service' for all non-Kindle books. FBreader is a nice cross-platfrom app (Android, Iphone, MacOS, web) I've used for years, though I recently moved off of it. It's both a highly customizable ebook reader, and a web-based annotations and book collections hosting service. The way you'd have to use it is,
you'd again have to use Google Drive (I'm not aware they support any other cloud storage solution). You'd DeDRM your Google, and other epub books in Calibre, then you'd upload all of them to your FBreader account (which will store the files in your Google drive). When you take annotations on those books, FBreader stores those in your Google Drive account as well, associating them with the books (so there's no external export), and syncing them seamlessly across devices. This actually works pretty well, like I said I've done it. Here's an interesting bonus, should you decide to choose your Boox device that you listed: FBreader is planning to specifically support Boox e-ink devices and their annotations app. They've already added support in a currently available beta app (see FBreader.org/news). No idea how all that will work, but worth knowing since you're considering Boox devices.
Option 4: Use an app that has its own service for synchronizing books, collections, and annotations, to Dropbox. The catch here is, all these apps can use Dropbox, but for your own convenience you'd want to use Calibre to DeDRM all your Google Books along with your other epubs, keep them in Calibre, and then publish the library to your Dropbox. If you wanted, you could even do the same with all your Kindle books, then you'd have everything running on the same app, annotations, syncing, and backup system. You'd no longer directly use the Google Books or Kindle services or readers, for anything other than initially buying books. Otherwise, you'd just be putting all books in Calibre, reading with one of these apps/services, and storing annotations and synced book files on your Dropbox storage.
Here are 3 I'm aware of that have good rep and use Dropbox:
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Moon+ Reader Pro. Syncs books, metadata such as collections and book details, and annotations to Dropbox with the paid edition. It's a nice reader, I've used it. Bonus items include:
that it also includes PDF markup and annotations features. It also direct-connects to Calibre library. This one might be worth checking out. I'm currently sold on pulling my books into the Kindle service as above for sync and annotations, but if I weren't doing that, I'd probably try this option since I already bought the paid lifetime Pro version of Moon+ years ago. One downside with moon is that last time I tried this, the annotations themselves aren't very 'rich' as in giving specific location links into the content, as the Kindle and Google Play apps do.
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Prestigio reader. Don't know much about this one, they have the capability to sync books/annotations to Dropbox, G-drive, Onedrive, though.
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Bookari. A French company I believe, they have a free Android app but also a monthly subscription service that not only hosts all your books/annotations in Dropbox, but gives you a web browser-based view of all your book content, mass export options for ALL your annotations, etc. I tried it briefly, about 2 years ago, but the monthly subscription cost (I think around $5 or $6/monthly) was more than I wanted to spend at the time. But might be worth checking out, see if it has the functionality you want. If I was really serious and doing a lot of annotations for work-related purpose, I'd be checking out this option since it has a lot richer features.
One last item--added as an afterthought. You mentioned using Readwise, one of this species of apps that can harvest annotations from Kindle and export to an app such as Evernote. I assume that also means you're an Evernote reader.
The most interesting, cross-platform one of these web content-harvesting 'snippet' apps I've seen recently, is called
Snippet. I'm actually doing a free trial of their paid subscription. It's quite interesting in that it knows how to harvest Kindle annotations and then export to EverNote, Onenote, and other formats like some of these other apps. But what I really like about it is, it's a general purpose web content snippet-gathering tool. It runs as an extension in your browser. Which means, not only can it harvest Kindle annotations from the online Kindle notebook, but if you used one of the above solutions that displays your annotations content in a web page (two examples that do that are: FBreader, and the Bookari service), presumably you could use Snippet to harvest your annotations from those web pages and pipe into Evernote as well. Just a thought.