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/providers/next-provider.tsx

@@ -0,0 +1,40 @@
+"use client";
+
+import { useState } from "react";
+import { QueryClientProvider } from "@tanstack/react-query";
+import { createTRPCClient, httpBatchLink } from "@trpc/client";
+import superjson from "superjson";
+import type { AppRouter } from "@repo/core-api";
+import { TRPCProvider } from "../client";
+import { getQueryClient } from "../query-client";
+
+function getBaseUrl() {
+  if (typeof window !== "undefined") return "";
+  return `http://localhost:${process.env.PORT ?? 3000}`;
+}
+
+export function NextTrpcProvider({
+  children,
+  trpcUrl = "/api/trpc",
+}: {
+  children: React.ReactNode;
+  trpcUrl?: string;
+}) {
+  const [queryClient] = useState(() => getQueryClient());
+  const [trpcClient] = useState(() =>
+    createTRPCClient<AppRouter>({
+      links: [
+        httpBatchLink({
+          url: `${getBaseUrl()}${trpcUrl}`,
+          transformer: superjson,
+        }),
+      ],
+    }),
+  );
+
+  return (
+    <TRPCProvider trpcClient={trpcClient} queryClient={queryClient}>
+      <QueryClientProvider client={queryClient}>{children}</QueryClientProvider>
+    </TRPCProvider>
+  );
+}