feat(22-02): build AddToThreadModal with thread picker and new thread flow

- Create AddToThreadModal with pick/create modes for thread selection
- Support existing thread selection with category display
- Support new thread creation with candidate in one step
- Pre-select session thread via catalogSessionThreadId
- Auto-switch to create mode when no active threads exist
- Wire AddToThreadModal at root layout level

src/client/routes/__root.tsx

@@ -11,6 +11,7 @@ import { useState } from "react";
 import { Toaster } from "sonner";
 import "../app.css";
 import { AddToCollectionModal } from "../components/AddToCollectionModal";
+import { AddToThreadModal } from "../components/AddToThreadModal";
 import { CatalogSearchOverlay } from "../components/CatalogSearchOverlay";
 import { ConfirmDialog } from "../components/ConfirmDialog";
 import { ExternalLinkDialog } from "../components/ExternalLinkDialog";
@@ -208,6 +209,8 @@ function RootLayout() {
 
 			{/* Add to Collection Modal */}
 			<AddToCollectionModal />
+			{/* Add to Thread Modal */}
+			<AddToThreadModal />
 			<Toaster position="bottom-right" richColors />
 
 			{/* Onboarding Wizard */}