fix(browser): persist interceptor across navigation

[cnYui]

Description

installInterceptor(pattern) only patched the current document before this change. If a caller installed the interceptor and then navigated, the new document lost the fetch/XHR monkey patch, so requests fired by the loaded page could not be captured.

This keeps the existing current-document evaluate() injection and, when the page exposes CDP, also registers the same interceptor source through Page.addScriptToEvaluateOnNewDocument. CDP registration is best-effort so non-CDP backends keep the previous behavior instead of failing interceptor setup.

Related issue: fixes #584

Type of Change

• 🐛 Bug fix
• ✨ New feature
• 🌐 New site adapter
• 📝 Documentation
• ♻️ Refactor
• 🔧 CI / build / tooling

Checklist

• I ran the checks relevant to this PR
• I updated tests or docs if needed
• I included output or screenshots when useful

Documentation (if adding/modifying an adapter)

• Added doc page under docs/adapters/ (if new adapter)
• Updated docs/adapters/index.md table (if new adapter)
• Updated sidebar in docs/.vitepress/config.mts (if new adapter)
• Updated README.md / README.zh-CN.md when command discoverability changed
• Used positional args for the command's primary subject unless a named flag is clearly better
• Normalized expected adapter failures to CliError subclasses instead of raw Error

N/A: this PR does not add or modify an adapter.

Screenshots / Output

$ npx vitest run --project unit src/browser/base-page.test.ts
Test Files  1 passed (1)
Tests       44 passed (44)

$ npx tsc --noEmit
# passed