I have a Kobo and it does OK. Nothing special.

You might try one of the larger Kobos to be able to read PDFs comfortably. The little ones might be a bit cramped with most PDFs. For html I've never tried that with Kobo, but a lot of people swear by the Android e-ink tablets from Onyx and Boox, though those are sometimes pricey!

I like my kobo

Also saying Kobo. I've got the Kobo Libra Colour and love it.

It's the only ereader I've ever owned but I used the spouse's Nook and Kindle a couple of times in the past and the Kobo kills it. Granted, we're talking about a nearly new release of the Kobo vs a 5+ year old Kindle so it's not a fair comparison.

Because of eInk and auto-sleep, the battery lasts me well over a month of casual reading (~30min before bed) with the occasional multi hour weekend session. Backlight is present and is totally readable in dark areas at <10% brightness; 100% brightness is like a supernova in your face. While the Libra Colour is not specifically a note-taking tablet like a reMarkable, it does just fine for quick notes/todo lists/etc but I did splurge on the ($60) stylus. There's a "notes" application that comes pre-installed.
eBook support for writing in margins (or over text), underline/circling, highlighting, etc is really nice but occasionally the highlight is flakey when trying to highlight the end of a paragraph. That seems to have been specific to certain epubs rather than an "always" thing, but it happens in around 20% of epubs I've used.

EDIT: Notes and highlights you do in an epub (and presumably other formats) are exportable to your PC via Calibre ("Annotations"). I love this because I like to highlight things I find interesting, particularly good quotes, and this gives me an easy way extract them while retaining a reference to which book it was and where exactly in the book it was. Example attached.

Seconding a Kobo. They have Overdrive (library) integration in the US and their eink and full color options are both great.

I came across this giant comparison table of eReaders last time I was researching an upgrade. While it doesn't list supported file types, anything running an android operating system that lets you download apps for reading from google play would meet your needs.

https://comparisontabl.es/e-readers/

I use my remarkable 2 for that. Pretty expensive compared to other typically ebook readers but I use it to take notes too and it's basically a pen and paper replacement for me.

Boox Go 7 Color II

Install KoReader on it (it runs Android so it's literally just installing a new app) and you've got the best reading experience out there