feat: add comprehensive request and error logging

Add logging infrastructure:
- RequestLoggingMiddleware: logs all requests with method, path, status, timing
- ExceptionLoggingMiddleware: catches and logs unhandled exceptions with stack traces
- configure_logging(): structured logging with configurable level via LOG_LEVEL env var

Add detailed auth flow logging:
- Login initiation
- Token exchange success/failure
- JWKS fetch success/failure
- Token verification
- User lookup/creation
- Database errors
- Final response

This enables tracing Internal Server Errors through the logs.

apps/api/src/main.py

@@ -1,4 +1,5 @@
 import logging
+import os
 
 from fastapi import FastAPI
 from fastapi.staticfiles import StaticFiles
@@ -12,10 +13,21 @@ from src.api.tool_types import router as tool_types_router
 from src.api.user_config import router as user_config_router
 from src.api.users import router as users_router
 from src.database import SessionLocal, init_database
+from src.logging_config import (
+    ExceptionLoggingMiddleware,
+    RequestLoggingMiddleware,
+    configure_logging,
+)
 from src.models.tool_type import ToolType
 
+# Configure logging early
+log_level = os.getenv("LOG_LEVEL", "INFO").upper()
+configure_logging(level=getattr(logging, log_level, logging.INFO))
+
 logger = logging.getLogger(__name__)
 app = FastAPI(title="Headquarter API")
+app.add_middleware(RequestLoggingMiddleware)
+app.add_middleware(ExceptionLoggingMiddleware)
 
 
 async def _table_exists(session, table_name: str) -> bool: