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FOSS alternative to Pocket?
(sh.itjust.works)
F-Droid is an installable catalogue of FOSS (Free and Open Source Software) applications for the Android platform. The client makes it easy to browse, install, and keep track of updates on your device.
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Wallabag is the most popular alternative, to my knowledge. I believe, it requires a server, though.
It doesn't but I do believe --have not checked a while-- that you have to pay for the service. It is "free" if you host, server price aside. On that you are right.