Which e-ink tablet would you recommend?

Remarkable 2 is the only one I have experience with, and I recommend it highly if you are comfortable exploring the community APIs and tools. It uses a proprietary cloud platform by default, which may not appeal to folks, but you can use ssh over usb to avoid their cloud entirely. I use a script based on https://github.com/subutux/rmapy to send the tablet pdf files with one command. The reading experience is excellent and the writing surface/pen are great for marking up documents as well. It's a magnificent paper notebook replacement that you can fairly easily put pdfs on. If you need on-tablet web browsing, other apps, or state of the art epub reading, I'd look elsewhere. For getting reading material off a backlit screen as though it were an endless stack of paper with arbitrary content, it's phenomenal.

I'm pretty happy with the Onyx BOOX.

https://news.ycombinator.com/item?id=27521248

Turns out I was wrong about security. Password recovery requires a separate cloud-based account. Setting a password does not.

ReMarkable isn’t perfect but I use it to read web articles. The issue I haven’t solved with my ReMarkable is finding an alternative to the default synchronization system. I’d love to use Plato for reading on the ReMarkable, but then I’d lose the synchronization.

Kobo devices have out of the box integration with Pocket, which Mozilla supports natively.

Proprietary tablet vs. a browser feature on the open web–which option would you take?

Kobo lets you install your own SW. There are open source reader SW for the Kobo, and they're better than Kobo's own reader.

What reader(s) do you like / recommend?

I've used FBReader, PocketBook (who sell their own ebook readers as well apparently), the NeoReader (default Onyx software), and have some familiarity with Kindle.

PocketBook enables some (but insufficient) metadata editing. The NeoReader has an excellent UI/UX generally on BOOX devices, but has no management capability.

I tend to have a large number of documents on my devices (1,000s). Management is critical.

I'm not sure what exactly you're arguing against.