[CYS on Core] Align the badge component in the themes intro screen

[albarin]

Submission Review Guidelines:

• I have followed the WooCommerce Contributing Guidelines and the WordPress Coding Standards.
• I have checked to ensure there aren't other open Pull Requests for the same update/change.
• I have reviewed my code for security best practices.
• Following the above guidelines will result in quick merges and clear and detailed feedback when appropriate.

Changes proposed in this Pull Request:

Closes #45282

How to test the changes in this Pull Request:

Using the WooCommerce Testing Instructions Guide, include your detailed testing instructions:

1. Ensure the WooCommerce Beta Tester plugin is installed and activated (available on this monorepo).
2. Head over to /wp-admin/tools.php?page=woocommerce-admin-test-helper and enable customize-store feature flag.
3. Go to WooCommerce > Home and click on Start customizing.
4. Check the active theme badge colors match with the active admin theme.
5. Go to wp-admin/profile.php and change the color Admin Color Scheme to another color and check the badge colors update accordingly.

Changelog entry

• Automatically create a changelog entry from the details below.

Significance

• Patch
• Minor
• Major

Type

• Fix - Fixes an existing bug
• Add - Adds functionality
• Update - Update existing functionality
• Dev - Development related task
• Tweak - A minor adjustment to the codebase
• Performance - Address performance issues
• Enhancement - Improvement to existing functionality

Message

CYS - Use the admin theme color to style the active theme badge component in the Intro page.

Comment

[github-actions]

Hi @gigitux, @nefeline, @woocommerce/woo-fse

Apart from reviewing the code changes, please make sure to review the testing instructions as well.

You can follow this guide to find out what good testing instructions should look like:
https://github.com/woocommerce/woocommerce/wiki/Writing-high-quality-testing-instructions

[github-actions]

Test Results Summary

Commit SHA: c477c99

Test 🧪	Passed ✅	Failed 🚨	Broken 🚧	Skipped ⏭️	Unknown ❔	Total 📊	Duration ⏱️
API Tests	259	0	0	2	0	261	0m 38s
E2E Tests	65	0	0	288	0	353	7m 32s

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To view the full API test report, click here.
To view the full E2E test report, click here.
To view all test reports, visit the WooCommerce Test Reports Dashboard.

[gigitux]

LGTM 🚀

[danielwrobert]

I activated 4 different admin themes (Default, Ocean, Ectoplasm, and Sunrise) and the badge updates with each one, as expected.

Nice work!