Support site settings writes through Core REST

[crazytonyli]

Note

I recommend reviewing this PR commit by commit.

Description

Application-password sites use BlogServiceRemoteCoreREST, but BlogService.updateSettingsForBlog only dispatches WP.com REST and XML-RPC. Saving a setting therefore sends no request and invokes neither callback, leaving loading indicators
active.

One big refactor in this PR is that callers now pass a BlogSettingsChanges containing only the values changed by the user. Previously, BlogService built a full settings snapshot from Core Data for every save, which could overwrite
unrelated settings. Writes are also serialized because UI controls can trigger multiple saves quickly.

The other main changes are:

1. BlogService.updateSettings writes supported fields through /wp/v2/settings and completes with exactly one callback for WP.com REST, Core REST, XML-RPC, and unavailable transports.
2. Core REST maps the site icon in both directions, and WordPressClient.updateSiteSettings replaces the cached settings after a save. The site-icon flow also updates the header without waiting for syncBlog, which has no Core REST path.

Testing instructions

On a self-hosted application-password site:

1. Change the Site Title and Tagline. Verify the loading indicator stops and the values persist after reopening Site Settings.
2. Rapidly toggle settings under Sharing and Discussion. Verify the latest values persist.
3. Update and remove the site icon. Verify the header refreshes and its loading indicator stops.
4. Regression-test settings saves on WP.com and XML-RPC sites.

[dangermattic]

	2 Warnings
⚠️	View files have been modified, but no screenshot or video is included in the pull request. Consider adding some for clarity.
⚠️	This PR is larger than 500 lines of changes. Please consider splitting it into smaller PRs for easier and faster reviews.

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[wpmobilebot]

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	App Name	WordPress
	Configuration	Release-Alpha
	Build Number	33591
	Version	PR #25865
	Bundle ID	org.wordpress.alpha
	Commit	4a4b15b
	Installation URL	31mgp3ipvcd50

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[wpmobilebot]

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

	App Name	Jetpack
	Configuration	Release-Alpha
	Build Number	33591
	Version	PR #25865
	Bundle ID	com.jetpack.alpha
	Commit	4a4b15b
	Installation URL	32i4gvjar6h9g

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