Restore the sidebar user menu and move the Settings link into it

[youknowriad]

Related issues

How AI was used in this PR

The whole PR was written with Claude Code: it reverted #3777, restored the previous user menu, and made the follow-up edits (Settings menu item, logged-out gear button). Code reviewed by the author.

Proposed Changes

This reverts the user-menu consolidation from #3777 and takes a different direction.

The consolidation replaced the sidebar footer's avatar + name menu with a plain "Settings" link, moving account actions into a Settings → Account tab. In practice that traded away two things: the at-a-glance identity in the sidebar, and one-click access to frequent actions (theme switching, log out), which now required navigating to a settings page.

This PR restores the previous user menu — avatar + display name opening a dropdown with the account email, profile link, documentation, issue reporting, and log out, alongside the quick theme toggle — and moves the "Settings" link inside that dropdown instead of keeping a separate footer button. Clicking your own avatar/name to find Settings is the conventional pattern, and it leaves a single, smaller footer control.

Behavior notes:

• The Settings → Account tab is removed again; the Settings page is back to the Preferences form only. Account actions live in the user menu, so nothing is duplicated in two places.
• When logged out (no dropdown available), a cog icon button next to the theme toggle keeps the Settings page reachable.

Testing Instructions

1. Run the agentic UI shell and log in with WordPress.com.
2. Check the sidebar footer: it should show your Gravatar and display name with a theme toggle beside it.
3. Open the menu: it should list your email, Settings, Edit WordPress.com profile, Documentation, Report an issue, and Log out. "Settings" should navigate to the Settings page, which should only contain the Preferences form (no Account tab).
4. Toggle the theme via the moon/sun button and verify the footer looks right in both light and dark.
5. Log out: the footer should show "Log in with WordPress.com" plus a cog button that still opens Settings.

Pre-merge Checklist

• Have you checked for TypeScript, React or other console errors?

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing 620e7ef vs trunk

app-size

Metric	trunk	620e7ef	Diff	Change
App Size (Mac)	1354.74 MB	1354.74 MB	0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	620e7ef	Diff	Change
load	1642 ms	1615 ms	27 ms	⚪ 0.0%

site-startup

Metric	trunk	620e7ef	Diff	Change
siteCreation	9054 ms	9052 ms	2 ms	⚪ 0.0%
siteStartup	4416 ms	4414 ms	2 ms	⚪ 0.0%

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Results are median values from multiple test runs.

Legend: 🟢 Improvement (faster) | 🔴 Regression (slower) | ⚪ No change (<50ms diff)