Allow provider configs to inject custom request-body fields

What feature would you like to see?

Add a config option (e.g., model_providers.<id>.extra_body) that lets us merge arbitrary JSON into the POST body for both Responses and Chat providers so we can turn on vendor-specific capabilities such as Anthropic’s thinking block.

Additional information

Right now Codex always sends the same minimal payload, which prevents enabling Claude’s extended thinking (thinking: { type: "enabled", budget_tokens: N }). A per-provider payload hook would unlock that while keeping defaults unchanged, ideally with validation that merges cleanly and preserves the existing fields.