Fix the loading sites UI in the share extensions

[crazytonyli]

Description

I started with fixing an issue where the share extensions show an "offline error" before showing the site list. Then decided to refactor the UI a little bit to make the fetching state inline, which aligns with most of the app UI.

Fetching	No sites	Sites	Failure

[dangermattic]

	2 Warnings
⚠️	This PR is larger than 500 lines of changes. Please consider splitting it into smaller PRs for easier and faster reviews.
⚠️	This PR is assigned to the milestone 27.1. This milestone is due in less than 4 days. Please make sure to get it merged by then or assign it to a milestone with a later deadline.

Generated by 🚫 Danger

[wpmobilebot]

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

	App Name	WordPress
	Configuration	Release-Alpha
	Build Number	33204
	Version	PR #25798
	Bundle ID	org.wordpress.alpha
	Commit	25be9bc
	Installation URL	0k476343qodeg

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

[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	33204
	Version	PR #25798
	Bundle ID	com.jetpack.alpha
	Commit	25be9bc
	Installation URL	3uddfc1id5bno

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

[jkmassel]

I tested this in the sim and it seems to work well!