There are two ways to add databases via iCloud
iCloud dedicated Strongbox folder
via iOS Files app
Method 1 – iCloud Native Strongbox Folder
For method 1, if you already have a database on your iCloud Drive, it needs to be in the specific Strongbox folder before it will automatically appear in the app. This is because Strongbox is only allowed to look in this folder and not at the rest of your iCloud drive.
The Strongbox folder should be in the root of your iCloud drive. If you do not see it there it is possible it has not yet been created. If you create a new iCloud database from the iOS app, it will create the folder and place the new database in there. You can create a new database by tapping the ‘+’ icon in the top right corner and selecting ‘New Database’.
Once the folder is created you can move any existing database you might have into that folder and it should appear (with maybe a little delay) in the app automatically.
Method 2 – iOS Files
You can always add a database that is anywhere in your iCloud drive via iOS Files. You just need to tap the + button, and choose Files when asked for the location…