I use wallabag.it for this. I don't actually self host it, I've been a paying subscriber to the maintainer's hosted service for a few years now and I've had no complaints. It hasn't had many new features lately, but it does do what I want it to.
It doesn't capture comments in fediverse threads (see here: https://app.wallabag.it/share/6813d1f1616096.02317152 ), and there are some websites where it doesn't detect the contents of the article, but it does work the vast majority of the time.
I'm not sure what you could do about a Nextcloud integration. You can export articles as epubs and pdfs; I've done that a few times and put the exported files on my Nextcloud server. But there are also a bunch of wallabag apps for your different devices, which is what I use to read articles on those devices.
edit: Oh, I forgot to add that you can generate an RSS feed of your unread articles. So that could be added to Nextcloud's RSS reader.