bug(playground): tools and structured output are lost when round-tripping between the playground and saved prompts

Describe the bug

Tool definitions and structured output schemas have no path through saved prompts. They live in playground state only, so they are dropped in both directions:

• playground -> prompt: "Save as prompt" / "Save as new prompt version" carries over the messages, but never writes tools or the structured output schema into prompt.config.
• prompt -> playground: opening a prompt in the playground returns only messages, so even a prompt whose config already contains a schema written by hand, or by an SDK following the Prompt Config docs. It opens with the schema panel empty.

The net effect is that any prompt iterated on in the playground silently loses its tools and schema the moment it is saved, which makes the playground unusable for the tool-calling and structured-output workflows it advertises.

Steps to reproduce

1. Open the playground, define a tool and a structured output schema.
2. Click Save as prompt and save.

1. Open the saved prompt and check its Config. No tools, no schema.

Second path, no playground involved:

1. Create a prompt whose config is the response_format example straight from the Prompt Config docs.

1. Open it in the playground — the structured output panel is empty, even though the schema is right there in the config.

Langfuse Cloud or self-hosted?

Self-hosted

If self-hosted, what version are you running?

v4.10.0

SDK and integration versions

Not applicable

Additional information

• Long-standing asks for this: #3735 (9 votes), #8457 — "Playground: Use response format stored in Langfuse prompt config", #6421. This last one is an idea I am currently working in a fork as it is very much needed for my job

• #14089 implemented the round-trip and was closed unmerged.

• Known scope limit to decide on: the nested OpenAI tools shape from the docs is a separate compatibility gap from the schema one

Are you interested in contributing a fix for this bug?

Yes