To check if the file was being shared between MKP and KP, I made a change to the passwords list in MKP, close the app and opened it in KP.
That DB is now visible in the iPhones ''Files' app and it has the KP icon. In KeePassium (KP) I was able to use Add Database to open that database after entering my usual MKP password. In MiniKeePass (MKP) I saved the active kdbx to files 'On my Phone'.
