Summary

• keep Agent.close() from stopping the browser event bus when keep_alive=True
• preserve the event queue and idle callback so CDP WebSocket handlers remain attached for the next agent run
• add close-lifecycle tests for both keep-alive and non-keep-alive browser sessions

Fixes #4374.

Test plan

• python -m py_compile browser_use/agent/service.py tests/ci/test_agent_close.py
• python -m pytest tests/ci/test_agent_close.py -q
• python -m ruff check browser_use/agent/service.py tests/ci/test_agent_close.py --no-fix
• git diff --check

Summary by cubic

Keeps the browser event bus alive during Agent.close() when keep_alive=True, preserving the event queue and idle callback so CDP WebSocket handlers persist into the next run. Adds tests for both keep-alive and non-keep-alive close behavior.

• Bug Fixes
  • Keep-alive: do not stop the event bus; preserve event_queue and _on_idle.
  • Non-keep-alive: still kill the browser session. Tests cover both modes.

^{Written for commit 856e3f2. Summary will update on new commits.}