How to use .schema.yml definition for two entities avoiding duplicated code
Solution
Here is a very good way to do this, with thanks to @sonfd for the link.
node.type.*.third_party.my_module: &amp;third_party_settings_alias
  type: mapping
  label: 'My Module'
  mapping:
    lots more lines here ...
    which I do not want to duplicate ... 

# Use saved alias to repeat the same settings for media.type
media.type.*.third_party.my_module:
  *third_party_settings_alias

That's all there is to it. All the settings for node.type are repeated for media.type