test(lana): cover VS Code web host

[peternhale]

PR overview

Stack 4 of 4. Depends on #953. Adds automated VS Code Web coverage and local browser-host tooling.

Changes made

• Add Playwright coverage that opens a sample log from Explorer in VS Code Web.
• Verify the analysis webview and populated Call Tree render.
• Add the local headless VS Code Web server and serve:web workflow.
• Run the web E2E suite for pull requests and retain Playwright diagnostics as CI artifacts.
• Keep Playwright output isolated from Jest, ESLint, and source control.

Type of change

• Test
• Chore

Related issues

related W-23939830

Validation

• pnpm typecheck
• pnpm test:ci
• pnpm lint
• pnpm build
• pnpm test:e2e:web: 1 passed
• Fork CI: all six jobs passed