Split august and yale integrations

[bdraco]

Proposed change

Yale and August product lines have split into two separate companies and the APIs, authentication methods, servers, and systems are diverging enough that the integration needs to be split into two.

The full transition plan is at https://github.com/home-assistant/home-assistant.io/pull/33890

Type of change

• [ ] Dependency upgrade
• [ ] Bugfix (non-breaking change which fixes an issue)
• [x] New integration (thank you!)
• [ ] New feature (which adds functionality to an existing integration)
• [ ] Deprecation (breaking change to happen in the future)
• [ ] Breaking change (fix/feature causing existing functionality to break)
• [ ] Code quality improvements to existing code or addition of tests

Additional information

• This PR fixes or closes issue: fixes #https://github.com/home-assistant/core/issues/124460
• This PR is related to issue:
• Link to documentation pull request: https://github.com/home-assistant/home-assistant.io/pull/33890

Checklist

• [x] The code change is tested and works locally.
• [ ] Local tests pass. Your PR cannot be merged unless tests pass
• [ ] There is no commented out code in this PR.
• [ ] I have followed the development checklist
• [ ] I have followed the perfect PR recommendations
• [ ] The code has been formatted using Ruff (ruff format homeassistant tests)
• [x] Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• [x] Documentation added/updated for www.home-assistant.io

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  Updated and included derived files by running: python3 -m script.hassfest.
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[bdraco]

Nearly all review comments above also apply to the August integration since that is where most of the code originates. While I've spent months cleaning it up, there is still some legacy there. I could spend a few more weeks cleaning up the code/tests.

Still, this one is a difficult position since if we don't ship this; all the Yale Home users will likely stop working again because the old API key we are using will stop working permanently.

Since all the branches going into the integration branch have been reviewed, I suggest we merge this and address the comments in a follow-up.

[balloob]

I agree. This should be included in the release to avoid breaking users instances.