Agentic UI: Don't start a site while a stop for it is still in flight

[bcotrim]

Related issues

• Found while testing Agentic UI: Add the Open in… split button to the preview toolbar #4365. No separate issue.

How AI was used in this PR

Claude Code traced the race and wrote the fix and tests. I found the repro (pressing a destination while a site is stopping) and reviewed the diff.

Proposed Changes

Starting a site while a stop for it is still in flight leaves the site down — the stop lands last — while the UI believes it started. Every "not running, so start it" path then tries again, and it loops; the site never comes up.

The guard goes in useStartSite rather than at any one call site, so it holds for all of them: the sidebar, the site dropdown, the preview's Start button, auto-start on launch, and anything opening a URL in the preview. A skipped start no longer shows the "Site started" toast.

Testing Instructions

1. Start a site, then stop it.
2. While it is still stopping, trigger a start — e.g. Open in… → phpMyAdmin in the preview toolbar, or the sidebar's Start.
3. The start is ignored and the site finishes stopping. Before this PR it entered a start loop and never came up (repeated Starting server for '<site>' in the terminal).
4. Once the stop has finished, starting works normally.
5. Stopping site A while starting site B is unaffected — the guard is per-site.

Pre-merge Checklist

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

🤖 Generated with Claude Code

[wpmobilebot]

📊 Performance Test Results

Comparing a57383e vs trunk

app-size

Metric	trunk	a57383e	Diff	Change
App Size (Mac)	1372.96 MB	1372.96 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	a57383e	Diff	Change
load	1064 ms	1038 ms	26 ms	⚪ 0.0%

site-startup

Metric	trunk	a57383e	Diff	Change
siteCreation	6527 ms	6507 ms	20 ms	⚪ 0.0%
siteStartup	2381 ms	2358 ms	23 ms	⚪ 0.0%

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Results are median values from multiple test runs.

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