OpenAI Support confirmed that function calling is the only structured output currently supported by gpt-4.1.
Response formats with json object / json schema are “not compatible with these models.”
They then tried to link me to an internal OpenAI document on Notion 
which I obviously did not have access to.
Editing April 25th, 2025 - gpt-4.1 and o4-mini both have all structured outputs you would expect in the playground, so OpenAI Support (an AI Agent) was wrong. Looks like there are quite a few inconsistencies.