I have a simple question - I'd like to change the value of this dropdown box programmatically (in Python) for a large number of layers in a large number of layer files.

The default setting for loading .lyr files into pro sets this to 'Layer has its own metadata'. This is also the case when loading programmatically via LayerFile("uri-to-layer.lyr") I want to run a Python script to reset this to 'Show metadata from data source (read-only)', as is possible in the Pro UI.
All of the methods and mechanisms in the Metadata class seem to be based around the assumption I want to do something with metadata for this layer. I do not! I want to make it read-only and show users the metadata stored in our spatial database. But, Metadata.isReadOnly is itself read only!
I then intend to re-save them as .lyrx files.
Any suggestions welcome.