Would a self-hosted archive/bookmarking tool fit the bill? I haven't used Wallabag so I can't do a great comparasion - but it looks like Reminiscence might fit the bill for what you're looking for
I used ArchiveBox but had some version migration issues with Docker which invalid my entire archive. It was also too resource-hogging for my cheap NAS. Then I looked into Reminiscence after but way to complicated to set-up for me.
Now I run SingleFile on my browser with Linkding (for "save-now-archive-later" thing) for temporary bookmarking. I usually archive 20-50 pages a day and push them to a h5ai instance (open directory) and manage them with Johnny Demical folder structure.
Maybe you can use archive.is (archive.today) to bypass the paywall, and then archive/outline it using Shiori or ArchiveBox? Unfortunately, archive.is isn't open-source and there's no alternative to that service.
I do find another project called Reminiscence, it works quite similar to ArchiveBox so the chance of bypassing paywalls is low, but still worth a try.
I'm not familiar with the product personally, but I did a little quick search because I wanted to help, and I was curious.
I came across one,
https://github.com/kanishka-linux/reminiscence
But it's a self-hosted solution, not sure if that will suit your needs.
I use a tool called Reminiscence (https://github.com/kanishka-linux/reminiscence). It allows me to bookmark sites but additionally archive them at that point in time as well, like my own Web Archive.org!
I've just read the first two paragraphs and I know what this is about. I've come to similar/far worse conclusions but too afraid to spell them out. I am just saving this should it be taken down (I am afraid it could be). BTW, I use this tool to save bookmarks locally. archive.is seem to be down.