refactor: type browser core

[jackwener]

Summary

• tighten browser-layer typing in src/types.ts, src/browser/page.ts, src/browser/cdp.ts, and daemon session reporting
• replace several browser-side any usages with explicit cookie/session/option types and local narrowing helpers
• keep dependent call sites compiling by preserving broad interface compatibility where needed

Validation

• npm run typecheck
• npm run build
• npx vitest run src/browser.test.ts src/browser/dom-snapshot.test.ts src/doctor.test.ts