feat(web): install Better-Auth client and create config (GRO-118)

- Add better-auth to apps/web/package.json dependencies
- Create apps/web/src/lib/auth-client.ts with createAuthClient config
- Export signIn, signOut, useSession from the client
- Add vite-env.d.ts for Vite client types

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/web/package.json

@@ -14,6 +14,7 @@
   "dependencies": {
     "@groombook/types": "workspace:*",
     "@tailwindcss/vite": "^4.2.2",
+    "better-auth": "^1.0.0",
     "lucide-react": "^0.577.0",
     "react": "^19.0.0",
     "react-dom": "^19.0.0",

apps/web/src/lib/auth-client.ts

@@ -0,0 +1,7 @@
+import { createAuthClient } from "better-auth/react";
+
+export const authClient = createAuthClient({
+  baseURL: import.meta.env.VITE_API_URL ?? "http://localhost:3000",
+});
+
+export const { signIn, signOut, useSession } = authClient;

apps/web/src/vite-env.d.ts

@@ -0,0 +1 @@
+/// <reference types="vite/client" />