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Syncthing-friendly apps?
(lemmy.ml)
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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Haven't tried it, since I only sync with my PC and cloud server. But I just checked up and Librera has an option to save progress and profiles to a custom directory, so I guess that would be the way.