There's only one e-ink device that might meet your needs, the Lenovo Yoga Book C930 dual screen laptop.
The Yoga Book C930 is a 10" laptop with one LCD screen and one e-ink screen. It's relatively expensive though and only has a couple of USB ports.
https://www.lenovo.com/us/en/laptops.../p/ZZIWZWBYB1J
You can read PDFs and take notes using the Onyx Boox devices and the Boyue devices like the Boyue Likebook, but as far as I know you can't connect them to other devices like a projector. I've tried both companies and wasn't satisfied. The problem IMO isn't the devices themselves, it's that most of the well known notetaking apps (OneNote, Evernote, etc) weren't designed for e-ink devices. The native notetaking apps on the devices work much better but they're niche apps designed for the e-ink device and don't have the features of well known apps like OneNote, Evernote and others.
The ReMarkable device I don't think can be connected to an external device at all and while I've read that the software is getting better it's still a "walled garden" so I'm not sure how easily notes can be exported except to the ReMarkable app.
Sadly, other than the Yoga Book C930 I don't think we'll ever see a device that does everything you'd like. The Microsoft Courier concept device might have been it, but they didn't release it back when everybody went nuts over the concept video and now the marketplace has moved on to LCD devices. IMO Microsoft (and Amazon, which allegedly developed a prototype Kindle Scribe device) really blew it when they didn't release those devices several years ago.