Make the output_schema stored in the prompt config in the playground and in experiments

[carlosagsmendes]

Describe the feature or potential improvement

Make the output_schema stored in the prompt config in the playground and in experiments:

I'm not aware of any way to use the output_schema stored in the prompt config without duplicating it

Additional information

No response

[jannikmaierhoefer]

Thanks @carlosagsmendes for adding this. We are tracking this here: https://github.com/orgs/langfuse/discussions/8457