Support manually syncing mirrors from the UI

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

Due to the use of webhooks which can fail to deliver, mirrors can sometimes develop conflicts or fail to sync with their corresponding feature branch.

### Describe the solution you'd like

The private mirrors UI should provide an option for users to manually trigger a sync of their mirror. Ideally this should include the ability to indicate the desired direction of the manual sync, the ability to force a sync to overwrite the desired direction in the case of conflicts, and potentially the ability to sync the mirror with the latest changes from the source repository.

### Describe alternatives you've considered

Additional pushes can be used to manually trigger syncs or in case of conflicts new mirrors can be created.

### Additional context

Due to the amount of options desired for this feature, sub-issues should be used to break down and track this work.