refactor: Backend core rewrite - WsHandler + WsManager + handler migration

- Add WsHandler base class, WsManager (connection tracking / event routing / buffering), WsResult
- Extract network.py (is_loopback_address) and context_utils.py (use_context) to eliminate duplication
- Migrate three handlers to api/ following the ws_* py naming convention
- Simplify run_ui.py WebSocket init from ~170 lines to ~10
- Update import paths in api.py, plugins.py, state_monitor.py

api/ws_webui.py

@@ -0,0 +1,32 @@
+from helpers.ws import WsHandler
+from helpers import extension
+
+
+class WsWebui(WsHandler):
+    """State synchronisation handler — the primary WebSocket endpoint for the UI."""
+
+    async def on_connect(self, sid: str) -> None:
+        await extension.call_extensions_async(
+            "webui_ws_connect", agent=None, instance=self, sid=sid
+        )
+
+    async def on_disconnect(self, sid: str) -> None:
+        await extension.call_extensions_async(
+            "webui_ws_disconnect", agent=None, instance=self, sid=sid
+        )
+
+    async def process(self, event: str, data: dict, sid: str) -> dict | None:
+        response_data: dict = {}
+
+        await extension.call_extensions_async(
+            "webui_ws_event",
+            agent=None,
+            instance=self,
+            sid=sid,
+            event_type=event,
+            data=data,
+            response_data=response_data,
+        )
+
+        # Return None (fire-and-forget) when no extension populated the response.
+        return response_data if response_data else None