Core Data: Migrate storage usage for ShippingMethodStore

[itsmeichigo]

Part of #14122

Description

This PR adds a small change to migrate the deprecated usage of writerDerivedStorage to use the new method performAndSave in ShippingMethodStore to ensure the write operations are handled by the writer operation queue.

Steps to reproduce

• Log in to a test store.
• Navigate to the Orders tab and select + to add a new order.
• Select one or more products.
• Select Add Shipping > Method.
• Confirm that the correct shipping methods are displayed.

Testing information

Tested with simulator iPhone 16 Pro iOS 18.1 and confirmed that shipping methods can be synced and displayed correctly after the changes.

Screenshots

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• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

Reviewer (or Author, in the case of optional code reviews):

Please make sure these conditions are met before approving the PR, or request changes if the PR needs improvement:

• The PR is small and has a clear, single focus, or a valid explanation is provided in the description. If needed, please request to split it into smaller PRs.
• Ensure Adequate Unit Test Coverage: The changes are reasonably covered by unit tests or an explanation is provided in the PR description.
• Manual Testing: The author listed all the tests they ran, including smoke tests when needed (e.g., for refactorings). The reviewer confirmed that the PR works as expected on all devices (phone/tablet) and no regressions are added.

[wpmobilebot]

📲 You can test the changes from this Pull Request in WooCommerce iOS by scanning the QR code below to install the corresponding build.

	App Name	WooCommerce iOS
	Build Number	pr14568-c6259ae
	Version	21.2
	Bundle ID	com.automattic.alpha.woocommerce
	Commit	c6259ae
	App Center Build	WooCommerce - Prototype Builds #11886

Automatticians: You can use our internal self-serve MC tool to give yourself access to App Center if needed.

[iamgabrielma]

Looks good and works well. Unrelated to your changes I found a bug/enhancement related to free shipping, logged it here: #14584

UI tests seems to have failed more than once, I've ran them again to see if it's flakiness or something else 👍