As far as things you can do with “Hey, Siri”, it’s just create new drafts, like “Using Drafts, create a note…”.
Technically, the Siri APIs are supposed to allow for third party notes apps to support appending, but I have worked with those APIs a number of times and never gotten them to work properly - and I have yet to see any other third party notes apps implement them, so I’m likely not the only one who has struggled with them.
Drafts also donate shortcuts for a number of things, which can be attached to your own custom voice shortcuts in iOS Settings > Siri, or can be added via the “Add to Siri” buttons in the app. These are for things like launching to dictation, or a specific workspace, or loading a certain draft. You can also add actions to Siri, but this functionality is somewhat limited by what a Siri Shortcut can do on iOS at the moment - since it can’t receive or output and data.