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.
In the app description:
"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..."
If that is the limitation, I wonder if they could get around that by using some type of bundle or archive. Regardless, thanks for the additional information.