Core Data: Migrate storage usage in SettingStore

[itsmeichigo]

Part of #14122

Description

This PR updates the storage usage in SettingStore:

• Replace the deprecated usage of writerDerivedStorage with the new method performAndSave to ensure write operations are handled in the same operation queue.
• Optimize fetch requests when upserting settings.

Steps to reproduce

Site settings are used in various features in the app, the most straightforward place to test would be the Product AI feature:

• Log out of the app to ensure that settings are cleared from the local storage.
• Log in to a test store that is Jetpack-connected with Jetpack plugin.
• Navigate to the Products tab > select + > Add product with AI.
• Enter a name or package photo for a physical product and proceed.
• Confirm that AI can generate product details with correct units for weight and dimensions.

Testing information

Tested on simulator iPhone 16 Pro iOS 18.1 and confirmed that features that require app settings like product creation AI, product details, and order details work as expected.

Screenshots

N/A

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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	pr14569-934e032
	Version	21.2
	Bundle ID	com.automattic.alpha.woocommerce
	Commit	934e032
	App Center Build	WooCommerce - Prototype Builds #11925

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

[hichamboushaba]

Nice work @itsmeichigo, code looks good, and works as expected, tested using iPhone 16 simulator, and confirmed that the site settings are also refreshed on app launch.