Responses API: Convert text.format JSON schema into the corresponding Chat Completions response_format

[boondocklabs]

Overview

Converts Responses API text.format JSON schema into the corresponding Chat Completions response_format.

ResponseFormatTextConfig docs

Additional information

Tests added and passing in test-chat.cpp

Requirements

• I have read and agree with the contributing guidelines
• AI usage disclosure: Yes, ChatGPT used for code exploration and analyzing logic, all code edits and validation performed manually.

[boondocklabs]

Second part of #26013. When this is merged, I will create a final PR with remaining streaming compatibility updates