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/errors.py

@@ -1,8 +1,7 @@
 """Shared exception types for the browser-cli client stack.
 
-Kept dependency-free so the transport/endpoint modules and ``client`` itself can
-import it without creating an import cycle. ``BrowserNotConnected`` is re-exported
-from :mod:`browser_cli.client` for backward compatibility.
+Kept dependency-free so the transport, endpoint, and client modules can import
+it without creating an import cycle.
 """
 from __future__ import annotations