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.

extension/manifest.json

@@ -1,7 +1,7 @@
 {
   "manifest_version": 3,
   "name": "browser-cli",
-  "version": "0.12.0",
+  "version": "0.12.1",
   "description": "Control your browser from the terminal or Python SDK",
   "permissions": [
     "tabs",