Fix Site Switcher screen not dismissing after adding self-hosted site

[pmusolino]

Fixes #24091

The Site Switcher screen wasn't being dismissed automatically after successfully adding a self-hosted site. This PR adds proper handling of the WPSigninDidFinishNotification notification to ensure the screen is dismissed when authentication completes.

Testing Instructions

1. Log in with a wp.com account
2. Open Site Switcher
3. Add a self-hosted site
4. Verify that after successful authentication, the Site Switcher screen is dismissed automatically.

Screen recording

Simulator.Screen.Recording.-.iPhone.16.Pro.-.2025-03-20.at.14.53.52.mp4

Regression Notes

1. Potential unintended areas of impact

2. What I did to test those areas of impact (or what existing automated tests I relied on)

3. What automated tests I added (or what prevented me from doing so)

PR submission checklist:

• I have completed the Regression Notes.
• I have considered adding unit tests for my changes.
• I have considered adding accessibility improvements for my changes.
• I have considered if this change warrants user-facing release notes and have added them to RELEASE-NOTES.txt if necessary.

Testing checklist:

• WordPress.com sites and self-hosted Jetpack sites.
• Portrait and landscape orientations.
• Light and dark modes.
• Fonts: Larger, smaller and bold text.
• High contrast.
• VoiceOver.
• Languages with large words or with letters/accents not frequently used in English.
• Right-to-left languages. (Even if translation isn’t complete, formatting should still respect the right-to-left layout)
• iPhone and iPad.
• Multi-tasking: Split view and Slide over. (iPad)

[dangermattic]

	1 Warning
⚠️	This PR is assigned to the milestone 25.9. The due date for this milestone has already passed. Please assign it to a milestone with a later deadline or check whether the release for this milestone has already been finished.

Generated by 🚫 Danger

[wpmobilebot]

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

	App Name	WordPress Alpha
	Configuration	Release-Alpha
	Build Number	pr24273-b3594ec
	Version	25.8
	Bundle ID	org.wordpress.alpha
	Commit	b3594ec
	App Center Build	WPiOS - One-Offs #11801

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

[wpmobilebot]

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

	App Name	Jetpack Alpha
	Configuration	Release-Alpha
	Build Number	pr24273-b3594ec
	Version	25.8
	Bundle ID	com.jetpack.alpha
	Commit	b3594ec
	App Center Build	jetpack-installable-builds #10825

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

[kean]

LGTM, but left one nit

[kean]

(nit) it's redundant

If your app targets iOS 9.0 and later or macOS 10.11 and later, and you used addObserver(_:selector:name:object:), you do not need to unregister the observer. If you forget or are unable to remove the observer, the system cleans up the next time it would have posted to it.