test: remove JS payload test + add non-async context test

[danielroe]

🔗 Linked issue

❓ 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)
• 🧹 Chore (updates to the build process or auxiliary tools and libraries)
• ⚠️ Breaking change (fix or feature that would cause existing functionality to change)

📚 Description

It's possible in future async context (#20918) might mask an issue with Nuxt instance being unavailable so until we enable it by default we should probably also keep testing it.

I've also removed the JS payload test matrix dimension as I think this is no longer required.

📝 Checklist

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

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