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Synology NASes have various apps for syncing mobile devices, such as DS Photo for uploading photos to Photo Station, Synology Drive for more of a Dropbox approach, and MailPlus for contacts, emails, etcs.

https://www.synology.com/en-nz/dsm/feature/photo_station https://www.synology.com/en-nz/dsm/feature/drive https://www.synology.com/en-nz/dsm/feature/mailplus

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

https://syncthing.net/

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.

Self-hosted VPN (if you're physically away from home) + directory sync app (in my case, SyncMe [at the moment; might switch to SyncThing]).

Smartphone integration isn't necessary for everyone (myself included), but I appreciate most people want it.