Support built-in GitHub notification management and real-time inbox

### **Feature summary**

Integrate native support for fetching, displaying, and managing GitHub notifications directly within the app's interface to eliminate context-switching.

### **What problem are you trying to solve?**

Developers use this app to streamline their workflow, yet keeping up with project updates still forces them to jump back into a web browser or check emails for GitHub notifications. When working across active repositories, critical interrupts like code review requests, failing CI pipelines, and direct `@mentions` are easily missed. This delay disrupts the continuous loop of building, reviewing, and tracking issues inside the application.

### **Proposed solution**

Introduce an inline notification inbox pane (leveraging the `/notifications` REST API endpoint) that allows users to seamlessly stay up to date without leaving the application. Core capabilities should include:

1. **Dedicated Notifications Panel:** A unified sidebar section or tab showing unread notifications grouped by repository, timestamp, or event type.
2. **High-Signal Filtering:** Quick-toggle filters to separate high-priority alerts (e.g., `reason:mention`, `reason:review_requested`, or `reason:ci_activity`) from standard thread updates.
3. **In-App Triage Actions:** Direct action buttons to mark notifications as `Done` (read), unsubscribe from noisy threads, or save items for later review.
4. **Intelligent State Sync:** Automatically mark notifications as read on GitHub when a user opens the corresponding session or issue inside the app, and respect standard GitHub poll interval headers to prevent rate-limiting.

### **Workflow impact**

This dramatically accelerates the day-to-day management loop for developers and engineering leads. It changes notifications from a disruptive multi-tab context switch into a low-friction, glanceable stream. Users can spot blocking code reviews or broken builds instantly and triage their entire inbox in a matter of seconds right where they do their core work.

### **Installation context**

User-level authentication (requiring `notifications` and `repo` OAuth/App scopes) to securely fetch individual user notification threads.

### **Additional context**

* The integration can take advantage of GitHub's optimized conditional polling via the `Last-Modified` and `If-Modified-Since` headers to ensure negligible performance and rate-limit overhead.
* Design-wise, the panel could mirror the clean, low-overhead triage flow found in native dashboards or the GitHub Mobile notification system.