Migrate browser tests to native @playwright/test

[smiggleworth]

Summary

Migrates this repo's browser-mode test suite off vitest browser-mode (@vitest/browser-playwright) onto native @playwright/test, following the reference pattern established in phase 1 (askrjs/askr-i18n#28). This decouples test:browser from vite-plus's internally pinned vitest version, which has caused recurring unrelated breakage.

What changed

• playwright.config.ts drives Chromium against the real vp dev server (this is an app repo with a real dev server, unlike the library-harness pattern from phase 1) — baseURL and webServer.url both pinned to 127.0.0.1:4179 to avoid the localhost-vs-127.0.0.1 webServer readiness race that silently timed out CI in phase 1; stdout/stderr piped and a generous startup timeout set proactively
• tests/browser/docs-search.test.tsx and marketing-layout.test.tsx → docs-search.spec.ts and marketing-layout.spec.ts, faithful ports that page.goto() real routes on the served site (rather than mounting an isolated component tree) and preserve every original assertion
• removed vitest.test.browser.config.ts, @vitest/browser-playwright, and the standalone playwright devDependency (now pulled in transitively by @playwright/test)
• removed the tests/browser/__screenshots__ directory — it was gitignored/untracked and unreferenced by any test (no toMatchScreenshot/screenshot assertions exist in the current suite), so nothing needed porting to toHaveScreenshot()
• test:browser/lint scripts updated accordingly

test:unit is untouched and still runs on vitest via vp test run.

Verification

• npm run fmt:check, lint, typecheck all pass
• npm run test:unit — 40 tests passing (vitest, unchanged)
• npm run test:browser — 41 tests passing (new Playwright suite: 1 docs-search + 40 marketing-layout route/viewport/theme combinations)
• npm run build (client build, llms docs, SSG, generated-output-contract) passes