Host the site preview at the dashboard layout so it persists across routes

[youknowriad]

Related issues

• Related to Agentic UI: Foundation #3646 (ports the cross-route preview persistence from the agentic UI redesign)

How AI was used in this PR

Implemented with Claude Code in a pair session: it ported and adapted the preview-persistence architecture from #3646 onto the split-preview implementation that landed in #3817, with human review of the approach, scope trims, and manual testing of the result.

Proposed Changes

Today the site preview is owned by the session view, so any navigation — switching sessions, opening Settings — unmounts the webview and the next visit pays a full reload (white flash, lost scroll position, cold page). This PR moves preview ownership up to the dashboard layout, as in the agentic UI redesign:

• Navigating between sessions of the same site keeps the preview exactly where it was — no reload, no flicker.
• Navigating to routes without a preview (Settings, site settings) slides the panel closed but keeps the last previewed site's webview warm, so coming back is instant.
• The panel's open/closed state and current path are now remembered across navigation instead of resetting per session. Closing the preview in one session keeps it closed in the next (intentional behavior change).
• Annotations submitted from the preview are routed to whichever session is currently on screen.

The split/animation/resize mechanics from #3817 are unchanged — they moved into a reusable PreviewSplitFrame component so the layout and the session view share them.

Testing Instructions

1. Open a session for a running local site, browse the preview to an inner page (e.g. /wp-admin/).
2. Switch to another session of the same site → the preview must not reload and keeps the page.
3. Switch to a session of a different local site → the panel stays open; the webview swaps to the new site.
4. Go to Settings → the panel slides closed. Return to the session → it reopens instantly with the same page (no reload).
5. Close the preview with the header toggle, switch sessions → it stays closed; the app-menu toggle works from any route.
6. Annotate + Submit in session A → message lands in A. Switch to session B and submit annotations → lands in B.
7. A live-environment session shows no preview and no toggle.
8. Drag and keyboard-resize the panel (arrows, Home/End on the focused handle); width persists across restarts.
9. Long Settings page still scrolls; verify both light and dark mode.

Pre-merge Checklist

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

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing 3e24200 vs trunk

app-size

Metric	trunk	3e24200	Diff	Change
App Size (Mac)	1354.74 MB	1354.75 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	3e24200	Diff	Change
load	1632 ms	1653 ms	+21 ms	⚪ 0.0%

site-startup

Metric	trunk	3e24200	Diff	Change
siteCreation	8025 ms	9028 ms	+1003 ms	🔴 12.5%
siteStartup	3915 ms	4432 ms	+517 ms	🔴 13.2%

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Results are median values from multiple test runs.

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