feat(api): add request logging middleware

Why:
- Need visibility into API usage and performance
- Need to track request method, path, status, and duration
- Helps debugging production issues

Changes:
- Added RequestLoggingMiddleware class
- Logs at appropriate level (INFO/WARNING/ERROR)
- Non-invasive, no logic changes

src/main.py

@@ -1,6 +1,10 @@
 """FastAPI app factory. Composes all domain routers and middleware."""
 
 import logging
+import time
+from starlette.middleware.base import BaseHTTPMiddleware
+from starlette.requests import Request
+from starlette.responses import Response
 
 from fastapi import FastAPI
 from fastapi.middleware.cors import CORSMiddleware
@@ -23,6 +27,34 @@ logging.basicConfig(
     datefmt="%Y-%m-%d %H:%M:%S",
 )
 
+logger = logging.getLogger(__name__)
+
+
+# ── Request Logging Middleware ─────────────────────────────────────
+
+class RequestLoggingMiddleware(BaseHTTPMiddleware):
+    """Log request method, path, status code, and duration."""
+
+    async def dispatch(self, request: Request, call_next) -> Response:
+        start = time.time()
+        method = request.method
+        path = request.url.path
+
+        response = await call_next(request)
+
+        duration = (time.time() - start) * 1000  # ms
+        status = response.status_code
+
+        # Log at appropriate level
+        if status >= 500:
+            logger.error("%s %s -> %d (%.1fms)", method, path, status, duration)
+        elif status >= 400:
+            logger.warning("%s %s -> %d (%.1fms)", method, path, status, duration)
+        else:
+            logger.info("%s %s -> %d (%.1fms)", method, path, status, duration)
+
+        return response
+
 
 def create_app() -> FastAPI:
     """Create and configure the FastAPI application.
@@ -48,6 +80,9 @@ def create_app() -> FastAPI:
         allow_headers=["*"],
     )
 
+    # Request logging
+    app.add_middleware(RequestLoggingMiddleware)
+
     # Register exception handlers
     app.add_exception_handler(ChunkingError, chunking_exception_handler)
     app.add_exception_handler(BenchmarkError, benchmark_exception_handler)