Earlier quoted context omitted.
You can't publish your own competing app. The desired behaviour requires running a background service (not allowed) that watches arbitrary folders (not allowed).
I think you lost the plot - you can publish a competing app that uses the Files app for sync, just like NextCloud does.
We see a NextCloud dev explaining that background uploads don't work herehttps://github.com/nextcloud/ios/issues/215
And we can see syncthing devs lamenting the many issues with an iOS client here https://github.com/syncthing/syncthing/issues/102
It may be the case that file eventing now works, but a quick check with an iOS dev friend suggests that the filesystem sandboxing is too restrictive to be meaningful anyway.
Further on this issue, consider that a functioning syncthing client is a node in a p2p network, so must be able to advertise and listen to requests in the background as well as the background jobs that NextCloud requires (as NextCloud is centralised it doesn't need node level co-ordination) - so a partially working NextCloud client is good enough, but a partially working Syncthing client is woefully broken.