core: HomeKit Controller fails to pair with LIFX beam

The problem

When attempting to pair my LIFX Beam directly to Home Assistant using the homekit_controller integration it requests the pairing code and then fails with the error message:

Incorrect HomeKit code. Please check it and try again.

Upon retrying with the exact same code I get:

An unhandled error occurred while attempting to pair with this device. This may be a temporary failure or your device may not be supported currently.

What version of Home Assistant Core has the issue?

core-2022.6.6

What was the last working version of Home Assistant Core?

No response

What type of installation are you running?

Home Assistant OS

Integration causing the issue

HomeKit_Controller

Link to integration documentation on our website

https://www.home-assistant.io/integrations/homekit_controller/

Diagnostics information

No response

Example YAML snippet

No response

Anything in the logs that might be useful for us?

**Log from Home Assistant Core**

2022-06-20 00:16:41 ERROR (MainThread) [homeassistant.components.homekit_controller.config_flow] Pairing attempt failed with an unhandled exception
Traceback (most recent call last):
File "/usr/src/homeassistant/homeassistant/components/homekit_controller/config_flow.py", line 362, in async_step_pair
pairing = await self.finish_pairing(code)
File "/usr/local/lib/python3.9/site-packages/aiohomekit/controller/ip/discovery.py", line 149, in finish_pairing
request, expected = state_machine.send(response)
File "/usr/local/lib/python3.9/site-packages/aiohomekit/protocol/__init__.py", line 226, in perform_pair_setup_part2
raise InvalidError("M5: not an error or a proof")
aiohomekit.exceptions.InvalidError: M5: not an error or a proof
2022-06-20 00:17:41 ERROR (MainThread) [homeassistant.components.homekit_controller.config_flow] Pairing attempt failed with an unhandled exception
Traceback (most recent call last):
File "/usr/src/homeassistant/homeassistant/components/homekit_controller/config_flow.py", line 362, in async_step_pair
pairing = await self.finish_pairing(code)
File "/usr/local/lib/python3.9/site-packages/aiohomekit/controller/ip/discovery.py", line 149, in finish_pairing
request, expected = state_machine.send(response)
File "/usr/local/lib/python3.9/site-packages/aiohomekit/protocol/__init__.py", line 226, in perform_pair_setup_part2
raise InvalidError("M5: not an error or a proof")
aiohomekit.exceptions.InvalidError: M5: not an error or a proof

### Additional information

_No response_