Auto-install Playwright Chromium when opening the annotation browser

[youknowriad]

Related issues

• Related to #

How AI was used in this PR

Claude Code investigated the /annotate failure, traced it to the annotation browser bypassing Studio's shared browser launcher, implemented the fix, and wrote it up. All code was reviewed by the author.

Proposed Changes

When a user runs /annotate, Studio opens a headed Playwright browser with the annotation inspector injected. If Playwright's managed Chromium was missing or had just been version-bumped (a common situation after a Playwright upgrade), this failed with a raw Executable doesn't exist ... Please run 'npx playwright install' error, leaving the user stuck unless they manually installed the browser.

Studio's screenshot and block-validation tools already handle this gracefully: they fall back across launch targets and auto-install Playwright's Chromium on demand. The annotation browser simply wasn't using that path — it launched Chromium directly.

This change routes the annotation browser through the same shared launcher, so a missing or outdated Chromium is now installed automatically (using the bundled Playwright version, avoiding any version drift) instead of surfacing a dead-end error. Users get a working annotation browser on first run without manual setup.

Testing Instructions

1. Remove Playwright's managed browser to simulate a fresh/post-upgrade machine: rm -rf ~/Library/Caches/ms-playwright (macOS).
2. Build the CLI: npm run cli:build.
3. Trigger the annotation browser via /annotate (or the open_annotation_browser tool) against a running Studio site.
4. Expected: Chromium is auto-installed and the annotation browser opens, with no manual npx playwright install step required.

Pre-merge Checklist

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

[wpmobilebot]

📊 Performance Test Results

Comparing 38c3d01 vs trunk

app-size

Metric	trunk	38c3d01	Diff	Change
App Size (Mac)	2334.13 MB	2334.13 MB	+0.00 MB	⚪ 0.0%

site-editor

Metric	trunk	38c3d01	Diff	Change
load	1696 ms	1757 ms	+61 ms	🔴 3.6%

site-startup

Metric	trunk	38c3d01	Diff	Change
siteCreation	8507 ms	8542 ms	+35 ms	⚪ 0.0%
siteStartup	3870 ms	3874 ms	+4 ms	⚪ 0.0%

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Results are median values from multiple test runs.

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