I don’t use pocket like services myself but when I’m looking for alternatives I like to start at alternativeto.net. It’s a great tool for questions like this.

Here’s a query I did for Pocket for you: https://alternativeto.net/software/pocket/

I self-hosted Wallabag for a while. It's nothing fancy but has most of the basic functionality you would expect.

Wallabag! I am using it for more than a year and it is great

I've been very happy with https://omnivore.app. It's not quite fully self-hosted yet, they're working on it. But I prefer it over wallabag.

Next cloud is very heavy for just this but the book marks plugin and floccus browser plugins do what I needed for pocket. I used it as a shared bookmark service and didn't really leverage the offline content.

Not exactly like Pocket, but I started using Linkding for basically a bookmark service. It has a browser extension and also an option to mark links as unread so that you can find them easier later. It works as a read later type of thing, but doesn't have offline sync etc.

Everytime I've tried such a thing the lack of proper mobile support stopped me. Most of my usage is mobile so having to copy paste urls to a webpage and save them doesn't really work for me.

Wallabag is what most people recommend, but I couldn't get on with it.

I just finished setting up Wallabag and it's great. And it really shines with Miniflux RSS with it's dedicated "save to Wallabag" button. I love it. Omnivore is great too but I wanted self host so if they ever have the full version self host able, I'll check it out again.

I'm using Shiori as my Pocket replacement, seems to do what I need.