Support alternative methods of interacting with private mirrors

### Is your feature request related to a problem?

Some users are working to integrate Private Mirrors App into a larger "open source portal" context, where they already have a web app and additional tooling around OSS contributions (like which projects are available for contributions, who is allowed to contribute, etc). They'd like to make use of the internals of PMA - the mirror lifecycle management and synchronization - but wrap this in their own web service.

### Describe the solution you'd like

The goal would be to make PMA "embeddable" in other applications. @ajhenry brainstormed a couple of options like creating a RPC client, making the app "import"-able as a package, or having a separate web service from the front end which could be called by another app. Not sure which has the highest effort/reward and would best meet the user need, so this requires more exploration and thought.

### Describe alternatives you've considered

_No response_

### Additional context

_No response_