Initial Checks

• I confirm that I'm using the latest version of Pydantic AI
• I confirm that I searched for my issue in https://github.com/pydantic/pydantic-ai/issues before opening this issue

Description

I expect you'd get a similar error message to #2861, as described in https://community.openai.com/t/how-to-solve-badrequesterror-400-item-rs-of-type-reasoning-was-provided-without-its-required-following-item-error-in-responses-api/1151686.

The underlying cause is that we are not currently parsing and sending back built-in tool calls and results:

Specifically, we're not handling these types of output:

        ResponseFileSearchToolCall,
        ResponseFunctionWebSearch,
        ResponseComputerToolCall,
        ImageGenerationCall,
        ResponseCodeInterpreterToolCall,
        LocalShellCall,
        McpCall,
        McpListTools,
        McpApprovalRequest,
        ResponseCustomToolCall,

(Not of all of them are relevant to built-in tools)

Example Code

Python, Pydantic AI & LLM client version

`main`