It allows iCloud or obsidian syncing. I tried to set it up with Dropbox because I didn’t trust iClouds conflict resolution and couldn’t get it to work.
I think that's a limitation of the Files API. In the least, I've yet to come across an app that allows syncing with third-party storage apps through Files. I've only seen one-way saving or using the file picker to retrieve a file.
"KeePassium can work both offline and with your favorite cloud provider.
There is no setup: pick your database through the familiar Files interface — and that's it. By integrating with the Files app, KeePassium supports almost all storage providers, including..."
One thing to note is that this requires manually pulling and pushing in Working Copy as well as paying to unlock pro features ($20 one-time payment) to push to a remote repository.
You can just save to a folder on your iOS device and push/pull changes with the app “working copy”, which is a full gift client. It costs a pretty penny though.