Summary

• fix the Home Assistant adapter so no-op state_changed events do not consume the per-entity cooldown
• update the cooldown timestamp only after _format_state_change(...) produces a real message
• add a regression test that proves a 20 -> 20 event no longer suppresses the following 20 -> 21 change

Closes #12062.

Testing

• python3 -m pytest -o addopts= tests/gateway/test_homeassistant.py