Send private DM notifications to the requester when media becomes available

### Description

I'm always frustrated when media availability notifications either have to be posted in a public server channel or require users to constantly check if their request is ready. Posting download completions in public channels creates unnecessary noise and compromises user privacy regarding what individual members are requesting and watching.

### Desired Behavior

Doplarr should send a direct, private Discord message (DM) exclusively to the user who made the request once their TV series, season, or movie has finished downloading and is available to watch.

- Privacy first: The notification goes straight to the requester's DMs rather than spamming a shared Discord channel.
- Requester tracking: The bot tracks the requester's Discord ID alongside the Sonarr/Radarr/Overseerr request and triggers the DM once the import event is completed.

### Additional Context

Similar Discord bots (like Requestrr) implement this behavior by notifying the user privately via DM upon completion. Implementing this in Doplarr would provide a much cleaner and more private user experience for shared servers.

### Search Existing Issues

- [x] Yes, I have searched existing issues.

### Code of Conduct

- [x] I agree to follow Doplarr's Code of Conduct.