Fix issue in signing into another WP.com account

[crazytonyli]

This PR is built on top of #23644.

This PR fixes an issue with having multiple WP.com accounts in the app. Here are steps to reproduce the issue.

1. Create a self-hosted site and connect it to WP.com account A.
2. Open Jetpack app and sign in using WP.com account B.
3. Add the self-hosted site in step 1.
4. Tap "Stats" of the self-hosted site. You'll see a "Log in" button here.
5. Tap the Log in button to sign in with WP.com account A.

Expected behaviour: the app displays Stats content after successful login.

Actual behaviour: the app is kind of messed up, because it incorrectly saves the second WP.com account as the default account.

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)

[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	pr23654-c3e32dd
	Version	25.4
	Bundle ID	com.jetpack.alpha
	Commit	c3e32dd
	App Center Build	jetpack-installable-builds #9824

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 WordPress Alpha by scanning the QR code below to install the corresponding build.

	App Name	WordPress Alpha
	Configuration	Release-Alpha
	Build Number	pr23654-c3e32dd
	Version	25.4
	Bundle ID	org.wordpress.alpha
	Commit	c3e32dd
	App Center Build	WPiOS - One-Offs #10782

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