Adjust the GitHub config flow

[ludeeus]

Proposed change

2023.12.0 showed that the progress step handling of this integration was not great, as it would no longer do anything (just keep loading forever).
While the frontend change now has been reverted, this should still change as it is a bug.

I've not marked this for the milestone as (from what I understand) the frontend change will not be re-reverted for a while.

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• 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 #
• This PR is related to issue:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
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• Tests have been added to verify that the new code works.

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• 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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  Updated by running python3 -m script.gen_requirements_all.
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• Untested files have been added to .coveragerc.

To help with the load of incoming pull requests:

• I have reviewed two other open pull requests in this repository.

[home-assistant]

Hey there @timmo001, mind taking a look at this pull request as it has been labeled with an integration (github) you are listed as a code owner for? Thanks!

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[joostlek]

Also wondering, what part of 2023.12 did uncover that this isn't working optimal?

[ludeeus]

This reverts the change in the frontend that showed the problem home-assistant/frontend#18939