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I was under the impression that ReMarkable in particular was pretty good about this. I believe they just run a custom Linux variant and you can even ssh into them. I was really considering getting one, but I think the bigger issue for me is the LiPo battery. You can’t take the thing apart without a heat gun because it’s held together with adhesive, so in a few years when the battery doesn’t hold a charge, you have an…
The iPad is much better at it. You just install Nextcloud on it and now all apps have support for saving to your own server
Regarding the Nextcloud's sync functionality on iOS, though: Does it support two-way sync? And do note-taking apps like Notability support it, too? Last time I checked, my impression had been that none of them does – which is a deal breaker for me, given that I'm a heavy user of Syncthing and have really gotten used to its instant two-way syncing functionality to keep all my devices up-to-date.