fix: enable stateless_http in add-on and fix runtime Python version

Enable stateless_http=True in the add-on's mcp.run() call, aligning it
with all other HTTP deployment modes (main_web, main_sse, main_oauth).
The add-on was missed when stateless mode was introduced in v6.4.0.

Without stateless mode, mcp-proxy connections require consistent
Mcp-Session-Id header forwarding. If the proxy fails to maintain session
state, the server either creates orphaned sessions (stale data) or
rejects requests silently — matching the symptoms in #585.

Also fix the runtime Docker image from Python 3.14 to 3.13 to match the
builder stage, which was causing ModuleNotFoundError for ha_mcp due to
mismatched site-packages paths (python3.13 vs python3.14).

Fixes #585

Author: Sergey

homeassistant-addon/Dockerfile

@@ -23,7 +23,7 @@ RUN --mount=type=cache,target=/root/.cache/uv \
     uv sync --locked --no-dev --no-editable
 
 # --- Runtime stage: clean image without uv ---
-FROM python:3.14-slim-bookworm@sha256:f0540d0436a220db0a576ccfe75631ab072391e43a24b88972ef9833f699095f
+FROM python:3.13-slim-bookworm@sha256:8092ae2ef67061f9db412458dbdce44dbf16748fb3cae5cdbd020f467a9712d0
 
 WORKDIR /app
 

homeassistant-addon/start.py

@@ -144,6 +144,7 @@ def main() -> int:
             port=port,
             path=secret_path,
             log_level="info",
+            stateless_http=True,
             uvicorn_config={"log_config": _get_timestamped_uvicorn_log_config()},
         )
     except Exception as e: