refactor: reorganize client transport and extension internals

- Split client, native, remote, serve, markdown, and SDK internals into focused packages with direct imports.
- Move local and remote transport framing/protocol helpers behind clearer module boundaries.
- Break up the extension injected DOM logic into a separate content dispatch bundle and dedicated content modules.
- Add explicit client handling for passive remote discovery without noisy PQ warnings.
- Keep behavior covered with updated unit, integration, and extension tests.

browser_cli/markdown/__init__.py

@@ -0,0 +1,8 @@
+"""Markdown rendering and HTML-to-Markdown conversion helpers."""
+from browser_cli.markdown.render import (
+  _clean_markdown_output,
+  _convert_html_to_markdown,
+  render_markdown,
+)
+
+__all__ = ["_clean_markdown_output", "_convert_html_to_markdown", "render_markdown"]