Update shipping class block to match new designs

[mdperez86]

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 #38044

How to test the changes in this Pull Request:

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

1. Got to /wp-admin/tools.php?page=woocommerce-admin-test-helper
2. Under Features tab make sure to enable product-block-editor
3. Then visit /wp-admin/admin.php?page=wc-admin&path=/add-product
4. Under Shipping tab make sure the Shipping class dropdown control follows the ACs described in Product Block Editor: Update shipping class block to match new designs #38044

[github-actions]

Hi , @woocommerce/mothra

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

[joshuatf]

Looks great and is testing well! All AC look good to me with the exception of the updated dropdown that we discussed tackling separately in our last grooming call.

LGTM! 🚢

[github-actions]

Test Results Summary

Commit SHA: 41cc294

Test 🧪	Passed ✅	Failed 🚨	Broken 🚧	Skipped ⏭️	Unknown ❔	Total 📊	Duration ⏱️
API Tests	267	0	0	2	0	269	0m 52s
E2E Tests	189	0	0	10	0	199	29m 55s

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To view the full API test report, click here.
To view the full E2E test report, click here.
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