fix(core): handle anyio.BrokenResourceError for client disconnects (#9358)

Catch BrokenResourceError alongside ClosedResourceError in streaming
response, logging middleware, and app exception handlers so client
disconnects are logged at info level instead of surfacing as 500s.

Datadog: https://us5.datadoghq.com/error-tracking/issue/4f57af0c-d558-11f0-a65d-da7ad0900000

🤖 Generated with [Letta Code](https://letta.com)

Co-authored-by: Letta <noreply@letta.com>

letta/server/rest_api/app.py

@@ -11,6 +11,7 @@ from functools import partial
 from pathlib import Path
 from typing import Optional
 
+import anyio
 import uvicorn
 
 # Enable Python fault handler to get stack traces on segfaults
@@ -415,6 +416,12 @@ def create_application() -> "FastAPI":
     # === Exception Handlers ===
     # TODO (cliandy): move to separate file
 
+    @app.exception_handler(anyio.BrokenResourceError)
+    @app.exception_handler(anyio.ClosedResourceError)
+    async def client_disconnect_handler(request: Request, exc: Exception):
+        logger.info(f"Client disconnected: {request.method} {request.url.path}")
+        return JSONResponse(status_code=499, content={"detail": "Client disconnected"})
+
     @app.exception_handler(Exception)
     async def generic_error_handler(request: Request, exc: Exception):
         # Log with structured context