Update "Social Sharing"

[kean]

I started working on https://linear.app/a8c/issue/CMM-557/add-quick-link-to-manage-connections-to-publishing-settings, realized it would require a bit of refactoring, decided to descope it, but kept the minor design improvements I made:

Before / After

[sonarqubecloud]

Quality Gate passed

Issues
1 New issue
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

[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	29545
	Version	PR #24953
	Bundle ID	org.wordpress.alpha
	Commit	d8cf2e0
	Installation URL	32gip154a6r4o

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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	29545
	Version	PR #24953
	Bundle ID	com.jetpack.alpha
	Commit	d8cf2e0
	Installation URL	7va6rlg9r6lug

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