Photos are synced in the background via location change events (and thus requiring Location permission). It can be a bit unreliable from time to time, but generally works. Contacts and calendars are synced in the background via iOS' CalDav/CardDav integration.
Nextcloud app also exposed itself as file provider in Files.app, so it's possible to use it in place of iCloud Drive for apps that use the appropriate API. (Unfortunately most apps use CloudKit, which sync over iCloud.)
Ah, I see this now. Me and my boyfriend tried switching to Nextcloud a few years ago, but this wasn't implemented on iOS yet so we had to look elsewhere. Nice to see this opened up, it's about time. Hopefully they'll reverse their sideloading opinions as well.
It really got a lot better over the past years indeed. I do miss support for Heic, recently NC just decided to upload Jpeg instead of Heic, and I have mixed feeling about that (Jpeg just works, the new pictures app is great because of it... But I would prefer to have heic and live images everywhere...).
Nextcloud app also exposed itself as file provider in Files.app, so it's possible to use it in place of iCloud Drive for apps that use the appropriate API. (Unfortunately most apps use CloudKit, which sync over iCloud.)