fix: persist active_remote_id in state for remote session restore

Remote sessions failed to reconnect after page refresh because
restoreState() and renderSheetList() didn't pass remoteId to
openSession(). Fix:

- state.py: add active_remote_id field to empty_state()
- main.py: extend StatePatch model to accept active_session and
  active_remote_id; update PATCH /api/state to selectively update
  only fields explicitly provided (using model_fields_set)
- app.js restoreState(): read state.active_remote_id and pass it
  as remoteId option so page-refresh reconnects remote sessions
- app.js openSession(): fire-and-forget PATCH /api/state to persist
  active_session + active_remote_id after successful connect
- app.js closeSession(): fire-and-forget PATCH /api/state to clear
  both fields so refresh doesn't try to reopen a closed session
- app.js renderSheetList(): add data-remote-id to sheet items and
  pass remoteId in click handler (previously called openSession(name)
  with no remoteId, routing remote sessions to local 404 endpoint)

Fixes: POST /api/sessions/paperclip-adapter/connect 404 when clicking
a remote session from the mobile bottom sheet or after page refresh.

muxplex/main.py

@@ -279,7 +279,9 @@ app.add_middleware(
 
 
 class StatePatch(BaseModel):
-    session_order: list[str]
+    session_order: list[str] | None = None
+    active_session: str | None = None
+    active_remote_id: str | None = None
 
 
 class HeartbeatPayload(BaseModel):
@@ -332,10 +334,21 @@ async def get_state() -> dict:
 
 @app.patch("/api/state")
 async def patch_state(patch: StatePatch) -> dict:
-    """Update session_order in the persistent state and return the updated state."""
+    """Update fields in the persistent state and return the updated state.
+
+    Only fields explicitly included in the request body are updated;
+    omitted fields are left unchanged. Supports: session_order,
+    active_session, active_remote_id.
+    """
     async with state_lock:
         state = load_state()
-        state["session_order"] = patch.session_order
+        changed = patch.model_fields_set
+        if "session_order" in changed:
+            state["session_order"] = patch.session_order
+        if "active_session" in changed:
+            state["active_session"] = patch.active_session
+        if "active_remote_id" in changed:
+            state["active_remote_id"] = patch.active_remote_id
         save_state(state)
         return state