Add Application Performance Monitoring (APM) with Prometheus metrics

- Backend: Implement Prometheus metrics collection
  - Add prometheus-client dependency
  - Create metrics utility module with HTTP request tracking counters, histograms, gauges
  - Implement MetricsMiddleware to track request latency, count, and active requests
  - Add /metrics endpoint to expose metrics in Prometheus text format
  - Normalize paths to prevent cardinality explosion (e.g., /api/{id} for UUIDs)
  - Exclude /metrics and /health from detailed tracking

- Frontend: Add web vitals and API metrics collection
  - Install web-vitals library (v4.0.0) for Core Web Vitals tracking
  - Create metrics utility module for FCP, LCP, CLS, INP, TTFB collection
  - Implement useTrackedFetch hook for automatic API call metrics (method, endpoint, status, duration)
  - Initialize web vitals tracking in App component on mount
  - Provide exportMetrics() for sending metrics to backend

- Testing:
  - Add comprehensive backend metrics tests (9 tests, 100% coverage)
  - Add comprehensive frontend metrics tests (10 tests)
  - All tests passing

- Documentation:
  - Expand Docs/Observability.md with complete APM section
  - Include metrics reference, integration examples (Prometheus, Datadog, NewRelic)
  - Add troubleshooting guide and best practices for cardinality management
  - Update Tasks.md to mark APM task as complete

Metrics exposed:
- bangui_http_requests_total: HTTP request count by method, endpoint, status
- bangui_http_request_duration_seconds: Request latency histogram
- bangui_http_active_requests: Active request gauge
- Web Vitals: CLS, FCP, INP, LCP, TTFB with ratings
- API metrics: endpoint, method, status, duration, timestamp

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>

backend/app/routers/metrics.py

@@ -0,0 +1,36 @@
+"""Prometheus metrics endpoint for BanGUI.
+
+Exposes collected metrics in Prometheus text format at GET /metrics.
+"""
+
+from __future__ import annotations
+
+import structlog
+from fastapi import APIRouter
+from starlette.responses import Response
+
+from app.utils.metrics import get_metrics, get_metrics_content_type
+
+log = structlog.get_logger()
+
+router = APIRouter()
+
+
+@router.get(
+    "/metrics",
+    tags=["observability"],
+    summary="Prometheus metrics endpoint",
+    description="Exposes application metrics in Prometheus text format (OpenMetrics)",
+    include_in_schema=False,
+)
+async def get_application_metrics() -> Response:
+    """Get Prometheus metrics.
+    
+    Returns:
+        Prometheus-formatted metrics as plain text.
+    """
+    log.debug("metrics_endpoint_accessed")
+    return Response(
+        content=get_metrics(),
+        media_type=get_metrics_content_type(),
+    )