Add the admin_body_class filter to the Customizer.

[afercia]

Trac ticket: https://core.trac.wordpress.org/ticket/65796#ticket

Use of AI Tools

None

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This Pull Request is for code review only. Please keep all other discussion in the Trac ticket. Do not merge this Pull Request. See GitHub Pull Requests for Code Review in the Core Handbook for more details.

[github-actions]

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Props afercia, mukesh27.

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[github-actions]

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[mukeshpanchal27]

Tested well!

The custom class my_custom_class appears correctly after pulling the changes from this PR.

Before:

After:

[afercia]

Thanks for your review @mukeshpanchal27 I would like to hear from @westonruter if there's any reason to not do this we may be missing.