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/package.json

@@ -0,0 +1,37 @@
+{
+  "name": "@repo/core-trpc",
+  "private": true,
+  "version": "0.0.0",
+  "type": "module",
+  "exports": {
+    ".": "./src/index.ts",
+    "./next": "./src/providers/next-provider.tsx",
+    "./tanstack": "./src/providers/tanstack-provider.tsx"
+  },
+  "scripts": {
+    "build": "tsc --noEmit",
+    "lint": "eslint .",
+    "typecheck": "tsc --noEmit",
+    "test": "vitest run --passWithNoTests"
+  },
+  "dependencies": {
+    "@repo/core-api": "workspace:*",
+    "@tanstack/react-query": "^5.66.0",
+    "@trpc/client": "^11.17.0",
+    "@trpc/react-query": "^11.17.0",
+    "@trpc/server": "^11.17.0",
+    "@trpc/tanstack-react-query": "^11.17.0",
+    "react": "^19.0.0",
+    "superjson": "^2.2.1"
+  },
+  "devDependencies": {
+    "@repo/core-eslint": "workspace:*",
+    "@repo/core-testing": "workspace:*",
+    "@repo/core-typescript": "workspace:*",
+    "@testing-library/jest-dom": "^6.5.0",
+    "@testing-library/react": "^16.0.0",
+    "@types/react": "^19.0.0",
+    "jsdom": "^25.0.0",
+    "vitest": "^3.0.0"
+  }
+}