Add Server-Timing header to streaming endpoint

Reports cache_check latency in the response header, visible in
browser DevTools Network tab for ongoing performance monitoring.

api/app.py

@@ -3,6 +3,7 @@ from datetime import datetime, timedelta
 import json
 import logging
 import logging.config
+import time
 from typing import Annotated, AsyncGenerator, Optional
 from api.auth import get_current_user
 from api.config import DEV_TIER_ORIGINS, PROD_TIER_ORIGINS, APP_ENV
@@ -456,10 +457,15 @@ async def stream_listing_geojson(
     else:
         limit = _rate_limit_config.geojson_stream_limit_cap
 
+    timings: list[str] = []
+
     # Build POI distances lookup if requested
     poi_distances_lookup = _build_poi_distances_lookup(user.email, query_parameters.listing_type) if include_poi_distances else None
 
+    t0 = time.monotonic()
     cached_count = get_cached_count(query_parameters)
+    timings.append(f"cache_check;dur={(time.monotonic() - t0) * 1000:.1f}")
+
     if cached_count is not None and cached_count > 0 and not include_poi_distances:
         app_metrics.geojson_cache_operations.add(1, {"result": "hit"})
         generator = _stream_from_cache(
@@ -482,6 +488,7 @@ async def stream_listing_geojson(
         headers={
             "Cache-Control": "no-cache",
             "X-Accel-Buffering": "no",  # Disable nginx buffering
+            "Server-Timing": ", ".join(timings),
         }
     )