Fix app-theme-color not following header color

[Nezz]

Proposed change

Fix app-theme-color not following header color when the default theme is used in dark mode with the default primary color. The bug was released in 2024.5 and was introduced in #20558.

It was incorrectly fixed in #20671, only covering cases where users override the primary color. With this proper fix, that workaround is no longer needed.

Type of change

• 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

1. Default theme, dark mode, default primary color
2. Default theme, dark mode, manually set primary color

Additional information

• This PR fixes or closes issue: fixes Browser Tab colour does not match Theme colour #20759
• This PR is related to issue or discussion:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• 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

[piitaya]

Thank you !