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/serve/logging.py

@@ -0,0 +1,16 @@
+"""Shared logging helpers for ``browser-cli serve``."""
+from __future__ import annotations
+
+from datetime import datetime
+from rich.console import Console
+
+console = Console()
+
+def log_request(addr: tuple, command: str, profile: str | None, status: str, error: str | None = None) -> None:
+  ts = datetime.now().strftime("%H:%M:%S")
+  addr_str = f"{addr[0]}:{addr[1]}"
+  profile_str = f"[dim]{profile}[/dim] " if profile else ""
+  if error:
+    console.print(f"[dim]{ts}[/dim] {addr_str} {profile_str}[cyan]{command}[/cyan] [red]{status}[/red] {error}")
+  else:
+    console.print(f"[dim]{ts}[/dim] {addr_str} {profile_str}[cyan]{command}[/cyan] [green]{status}[/green]")