feat: use new nitropack render response

[danielroe]

🔗 Linked issue

nuxt/framework#6042

❓ Type of change

• 📖 Documentation (updates to the documentation or readme)
• 🐞 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)
• ⚠️ Breaking change (fix or feature that would cause existing functionality to change)

📚 Description

This aligns Bridge further with current Nuxt 3 nitropack render response handler, including calling render:html and using a render handler.

📝 Checklist

• I have linked an issue or discussion.
• I have updated the documentation accordingly.