Enable Code use with Real Browser

[kalil0321]

Summary by cubic

Enable CodeAgent to use a real Chrome browser and protect the default profile by copying it (and Local State) to a temp user-data directory. Also ensures provided BrowserSession instances are correctly started.

• New Features

  • Automatically copies the selected Chrome profile to a temp user-data dir, including “Local State”, to avoid corrupting the default profile.
  • Applies only to Chrome channels; Edge and others keep their existing behavior.
  • Updated real-browser docs with an asyncio main entry point.

• Bug Fixes

  • If a BrowserSession is provided, start it when needed to attach watchdogs once (no duplicate attachments).
  • Adjusted tests to validate temp-dir copying for Chrome and no copying for Edge.

^{Written for commit ef842fd02905ed2a141d5f9e57ca7af1f2c49733. Summary will update automatically on new commits.}

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