CI: make Playwright install deterministic and cache browser downloads

[nicoburns]

Summary

Removes a source of nondeterminism from the two Playwright CI jobs ("Playwright | Windows" and "Playwright | ") and caches the browser downloads.

• Both jobs ran npm ci followed by npm install -D @playwright/test, which re-resolved @playwright/test to the newest version matching the ^1.56.1 range — silently overriding the lockfile, so every CI run could get a different Playwright runner + browser build. The stray npm install line is removed so npm ci + the lockfile fully determine the version, and @playwright/test is pinned exactly ("1.56.1", no caret) in packages/playwright-tests/package.json (lockfile regenerated) so upgrades are explicit.

• Only Chromium is used (see projects in playwright.config.js), so npx playwright install becomes npx playwright install chromium (no --with-deps; the Linux job already installs system deps via cache-apt-pkgs-action).

• Adds an actions/cache@v5 step for the Playwright browser directory in both jobs, keyed on runner.os + hashFiles('packages/playwright-tests/package-lock.json'):

  • Windows: ~\AppData\Local\ms-playwright
  • Linux/macOS (matrix job): ~/.cache/ms-playwright / ~/Library/Caches/ms-playwright

  On cache hit, npx playwright install chromium no-ops (it skips already-downloaded browsers).

Verified locally: npm ci && npx playwright install chromium resolves 1.56.1 matching the lockfile. actionlint reports no new findings on the workflow (only preexisting warnings about custom warp runner labels and a Swatinem/rust-cache input).

Link to Devin session: https://dioxus.staging.devinenterprise.com/sessions/266de4d3e2bd42208aed86ad92cce74d
Open in Devin Desktop: https://dioxus.staging.devinenterprise.com/desktop/session/266de4d3e2bd42208aed86ad92cce74d?variant=devin-insiders
Requested by: @nicoburns

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