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>

pnpm-lock.yaml

@@ -86,6 +86,9 @@ importers:
       '@tailwindcss/vite':
         specifier: ^4.2.2
         version: 4.2.2(vite@6.4.1(@types/node@22.19.15)(jiti@2.6.1)(lightningcss@1.32.0)(terser@5.46.1)(tsx@4.21.0))
+      better-auth:
+        specifier: ^1.0.0
+        version: 1.5.6(@opentelemetry/api@1.9.1)(react-dom@19.2.4(react@19.2.4))(react@19.2.4)(vitest@3.2.4(@types/node@22.19.15)(jiti@2.6.1)(jsdom@26.1.0)(lightningcss@1.32.0)(terser@5.46.1)(tsx@4.21.0))
       lucide-react:
         specifier: ^0.577.0
         version: 0.577.0(react@19.2.4)
@@ -133,7 +136,7 @@ importers:
         specifier: ^26.1.0
         version: 26.1.0
       typescript:
-        specifier: ^5.7.3
+        specifier: ^5.9.3
         version: 5.9.3
       typescript-eslint:
         specifier: ^8.20.0