Restore accessory state into pairing using new HKC methods (#75276)

homeassistant/components/homekit_controller/__init__.py

homeassistant/components/homekit_controller/config_flow.py

homeassistant/components/homekit_controller/connection.py

...assistant/components/homekit_controller/device_trigger.py

homeassistant/components/homekit_controller/diagnostics.py

homeassistant/components/homekit_controller/manifest.json

homeassistant/components/homekit_controller/storage.py

requirements_all.txt

requirements_test_all.txt

tests/components/homekit_controller/common.py

tests/components/homekit_controller/test_config_flow.py

tests/components/homekit_controller/test_diagnostics.py

tests/components/homekit_controller/test_init.py

tests/components/homekit_controller/test_storage.py