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Syncthing may be used to sync remotely the relevant directories. It's multiplatform and has a Android app too (still not iOS though).

FolderSync is another excellent option that might mesh better with your existing setup.

I second this. I use FolderSync Pro to sync with Nextcloud. Straightforward setup and quite reliable.

How does it compare with the Syncthing companion app, which is 100% open source and ad free?

Not sure, I have not used Syncthing yet.