feat: Add metrics instrumentation for queue, health, and database operations

Implement Prometheus metrics to populate empty Grafana dashboard panels.

## Phase 1: Queue Size Metrics ✅
**File**: `processor.py`
- Track vector sync queue depth in real-time
- Update metric after receiving and processing each document
- Update metric during timeout (empty queue)
- Enables: "Processing Queue Depth" panel

## Phase 2: Health Check Metrics ✅
**File**: `app.py`
- Add Nextcloud connectivity check with timing
- Add Qdrant health check with timing
- Record dependency health status (up/down)
- Record health check duration
- Enables: 4 health status panels + health check duration panel

## Phase 3: Database Operation Metrics (Partial) ⏳
**File**: `storage.py`
- Instrument `store_refresh_token()` method
- Track SQLite INSERT operation timing and success/error status
- Enables: Partial data for database operation latency panel

## Metrics Now Exposed

### Queue Metrics:
- `mcp_vector_sync_queue_size` - Real-time queue depth

### Health Metrics:
- `mcp_dependency_health{dependency="nextcloud"}` - UP/DOWN status
- `mcp_dependency_health{dependency="qdrant"}` - UP/DOWN status
- `mcp_dependency_check_duration_seconds{dependency}` - Health check latency

### Database Metrics:
- `mcp_db_operations_total{db="sqlite",operation="insert"}` - Operation count
- `mcp_db_operation_duration_seconds{db="sqlite",operation="insert"}` - Operation latency

## Dashboard Impact

**Panels Now Populated** (7/34 panels):
- ✅ Processing Queue Depth
- ✅ Nextcloud Health
- ✅ Qdrant Health
- ✅ Health Check Duration
- ✅ Database Operation Latency (partial)
- ✅ Vector sync panels (already working from PR #292)

**Panels Still Empty** (remaining work):
- ⏳ OAuth panels (4): Token validations, exchanges, cache hit rate, refresh ops
- ⏳ MCP tool panels (3): Call volume, error rates, execution duration
- ⏳ Database panel: Needs more SQLite operations instrumented (~29 remaining)

## Testing

Verified metric definitions exist and will be recorded on next deployment.

## Next Steps

Phase 4: OAuth token metrics (unified_verifier.py, context_helper.py, storage.py)
Phase 5: MCP tool metrics (all server/*.py files with @mcp.tool())
Phase 3 completion: Remaining 29 database operations in storage.py

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

nextcloud_mcp_server/app.py

@@ -1,5 +1,6 @@
 import logging
 import os
+import time
 from collections.abc import AsyncIterator
 from contextlib import AsyncExitStack, asynccontextmanager
 from dataclasses import dataclass
@@ -44,6 +45,10 @@ from nextcloud_mcp_server.observability import (
     setup_metrics,
     setup_tracing,
 )
+from nextcloud_mcp_server.observability.metrics import (
+    record_dependency_check,
+    set_dependency_health,
+)
 from nextcloud_mcp_server.server import (
     configure_calendar_tools,
     configure_contacts_tools,
@@ -1205,12 +1210,35 @@ def get_app(transport: str = "sse", enabled_apps: list[str] | None = None):
         checks = {}
         is_ready = True
 
-        # Check Nextcloud host configuration
+        # Check Nextcloud host configuration and connectivity
         nextcloud_host = os.getenv("NEXTCLOUD_HOST")
         if nextcloud_host:
             checks["nextcloud_configured"] = "ok"
+            # Try to connect to Nextcloud
+            start_time = time.time()
+            try:
+                async with httpx.AsyncClient(timeout=2.0) as client:
+                    response = await client.get(f"{nextcloud_host}/status.php")
+                    duration = time.time() - start_time
+                    if response.status_code == 200:
+                        checks["nextcloud_reachable"] = "ok"
+                        set_dependency_health("nextcloud", True)
+                    else:
+                        checks["nextcloud_reachable"] = (
+                            f"error: status {response.status_code}"
+                        )
+                        set_dependency_health("nextcloud", False)
+                        is_ready = False
+                    record_dependency_check("nextcloud", duration)
+            except Exception as e:
+                duration = time.time() - start_time
+                checks["nextcloud_reachable"] = f"error: {str(e)}"
+                set_dependency_health("nextcloud", False)
+                record_dependency_check("nextcloud", duration)
+                is_ready = False
         else:
             checks["nextcloud_configured"] = "error: NEXTCLOUD_HOST not set"
+            set_dependency_health("nextcloud", False)
             is_ready = False
 
         # Check authentication configuration
@@ -1238,20 +1266,29 @@ def get_app(transport: str = "sse", enabled_apps: list[str] | None = None):
         qdrant_url = os.getenv("QDRANT_URL")  # Only set in network mode
 
         if vector_sync_enabled and qdrant_url:
+            start_time = time.time()
             try:
                 async with httpx.AsyncClient(timeout=2.0) as client:
                     response = await client.get(f"{qdrant_url}/readyz")
+                    duration = time.time() - start_time
                     if response.status_code == 200:
                         checks["qdrant"] = "ok"
+                        set_dependency_health("qdrant", True)
                     else:
                         checks["qdrant"] = f"error: status {response.status_code}"
+                        set_dependency_health("qdrant", False)
                         is_ready = False
+                    record_dependency_check("qdrant", duration)
             except Exception as e:
+                duration = time.time() - start_time
                 checks["qdrant"] = f"error: {str(e)}"
+                set_dependency_health("qdrant", False)
+                record_dependency_check("qdrant", duration)
                 is_ready = False
         elif vector_sync_enabled:
             # Using embedded Qdrant (memory or persistent mode)
             checks["qdrant"] = "embedded"
+            set_dependency_health("qdrant", True)
 
         status_code = 200 if is_ready else 503
         return JSONResponse(