ESLint Flat Config

[silamon]

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Proposed change

Convert the eslint lint and format to use the flat config configuration. (The current configuration is deprecated in eslint 9.) Still awaits an eslint release so we don't need to use the latest eslint dev.

Type of change

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

Example configuration

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue or discussion:
• Link to documentation pull request:

Checklist

• [x] The code change is tested and works locally.
• [x] There is no commented out code in this PR.
• [ ] Tests have been added to verify that the new code works.

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

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