Add support for model_reasoning_effort parameter to control thinking budget

[SaladDay]

Problem

Currently, the codex MCP tool only supports specifying the model parameter, but doesn't allow controlling the model_reasoning_effort configuration. This means all tasks use the same thinking budget defined in ~/.codex/config.toml, which is suboptimal for different task complexities.

Use Case

Different tasks require different levels of reasoning:

• Simple tasks (e.g., "add a print statement", "fix typo"): low or medium reasoning effort is sufficient and faster
• Complex tasks (e.g., "refactor architecture", "debug race condition"): high or xhigh reasoning effort provides better quality

Currently, users must either:

1. Manually edit ~/.codex/config.toml before each task (cumbersome)
2. Create multiple profiles (requires pre-configuration and doesn't scale)
3. Accept suboptimal performance (waste time on simple tasks or get poor results on complex ones)

Proposed Solution

Add a reasoning_effort parameter to the codex tool that maps to Codex CLI's -c model_reasoning_effort="..." option:

@mcp.tool()
async def codex(
    PROMPT: Annotated[str, "Task instruction"],
    cd: Annotated[Path, "Workspace root directory"],
    # ... existing parameters ...
    reasoning_effort: Annotated[
        Optional[str], 
        "Reasoning effort level: 'low', 'medium', 'high', 'xhigh'. Controls thinking budget for the task."
    ] = None,
) -> dict:
    # ...
    if reasoning_effort:
        cmd.extend(["-c", f'model_reasoning_effort="{reasoning_effort}"'])

Example Usage

# Quick fix - use low reasoning
mcp.call_tool("codex", {
    "PROMPT": "Add error logging to line 42",
    "cd": "/path/to/project",
    "reasoning_effort": "low"
})

# Complex refactoring - use xhigh reasoning
mcp.call_tool("codex", {
    "PROMPT": "Refactor the authentication system to support OAuth2",
    "cd": "/path/to/project", 
    "reasoning_effort": "xhigh"
})

Benefits

1. Performance: Faster responses for simple tasks
2. Quality: Better results for complex tasks
3. Cost efficiency: Avoid unnecessary compute on trivial operations
4. Flexibility: Claude Code can dynamically adjust reasoning budget based on task complexity

Additional Context

The Codex CLI already supports this via -c model_reasoning_effort="...". This feature request simply exposes that capability through the MCP interface, similar to how the model parameter is already exposed.