Fix #21473: Do not show the login screen if the user is already logged in

[crazytonyli]

Fixes #21473

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. 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.

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📲 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	pr24241-cca105f
	Version	25.8
	Bundle ID	org.wordpress.alpha
	Commit	cca105f
	App Center Build	WPiOS - One-Offs #11705

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[pmusolino]

Thank you @crazytonyli for fixing this.

Everything works as expected 👍

However, I am encountering a problem not strictly related to this issue, namely that when I delete the website, the deletion view remains open, while below there is the view to add a new website. It is not blocking, because clicking outside the view dismisses it, however, the UX needs to be improved. Opened an issue here.

[crazytonyli]

@pmusolino Good catch! I can look into the issue later.