feat: update example app to Nuxt 4 and SSR for Vue

[colinscz]

🔗 Linked issue

❓ Type of change

• 📖 Documentation (updates to the documentation, readme or JSdoc annotations)
• 🐞 Bug fix (a non-breaking change that fixes an issue)
• 👌 Enhancement (improving an existing functionality like performance)
• ✨ New feature (a non-breaking change that adds functionality)
• 🧹 Chore (updates to the build process or auxiliary tools and libraries)
• ⚠️ Breaking change (fix or feature that would cause existing functionality to change)

📚 Description

📝 Checklist

• I have linked an issue or discussion.
• It's submitted to the main branch
• When resolving a specific issue, it's referenced in the PR's title (e.g. fix #xxx[,#xxx], where "xxx" is the issue number)
• I have updated the documentation accordingly.
• All tests are passing
• New/updated tests are included
• I have updated the "upcoming" section inside docs/changelog.md explaining the changes I contributed

If adding a new feature, the PR's description includes:

• A convincing reason for adding this feature (to avoid wasting your time, it's best to open a suggestion issue first and wait for approval before working on it)

Other information: