As someone also building constrained decoders against JSON [1], I was hopeful to see the same but I note the following from their documentation:

  The model can choose to call a function; if so, the content will be a stringified JSON object adhering to your custom schema (note: the model may generate invalid JSON or hallucinate parameters).

So sadly, it is just fine tuning. There's no hard biasing applied :(. You were so close, but so far OpenAI!

[1] https://github.com/newhouseb/clownfish

[2] https://platform.openai.com/docs/guides/gpt/function-calling