When they go bust they will sell your data.

FreshRSS has some too: https://freshrss.github.io/FreshRSS/en/users/08_sharing_services.html

Wallabag is nice - it’s making an archive of the page you’re saving and I think you can export it as pdf/epub to read it on any device.

I don’t know about freshrss - I’ve used it a few years ago - but miniflux (another self hosted RSS reader) has integrations with a lot of tools, some of which are bookmark managers. I’ve set up mine with Linkding and it woks just as you described.