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/src/content-dispatch.ts

@@ -0,0 +1,7 @@
+import { contentDispatch } from './content/dispatch';
+
+declare global {
+  var browserCliContentDispatch: typeof contentDispatch | undefined;
+}
+
+globalThis.browserCliContentDispatch = contentDispatch;