feat(core-trpc): scaffold tRPC client with React Query providers

- createTRPCContext + useTRPC hook for typed client access
- NextTrpcProvider with SSR-safe absolute URL resolution
- TanstackTrpcProvider for TanStack Start apps
- /api/trpc catch-all route handler in web-next
- Wire NextTrpcProvider into app providers
- Add @repo/core-trpc to transpilePackages

packages/core-trpc/src/query-client.ts

@@ -0,0 +1,22 @@
+import { QueryClient } from "@tanstack/react-query";
+
+let clientQueryClient: QueryClient | undefined;
+
+const defaultOptions = {
+  queries: {
+    staleTime: 30 * 1000,
+    refetchOnWindowFocus: false,
+  },
+};
+
+export function getQueryClient(): QueryClient {
+  if (typeof window === "undefined") {
+    // Server: always create a new instance per request
+    return new QueryClient({ defaultOptions });
+  }
+  // Browser: singleton
+  if (!clientQueryClient) {
+    clientQueryClient = new QueryClient({ defaultOptions });
+  }
+  return clientQueryClient;
+}