Add reasoning or service_mode to Otel Logs

What version of Codex CLI is running?

v0.128.0

What subscription do you have?

Enterprise

Which model were you using?

gpt-5.5

What platform is your computer?

Darwin arm

What terminal emulator and version are you using (if applicable)?

iTerm2

What issue are you seeing?

Otel logs being sent from Codex CLI doesn't contain the reasoning or service_mode set by the user. Since these settings influence the token usage, we want this data to be visible either on Admin dashboard or in the otel logs/traces/metrics, so we can nudge the users to have the right settings.

What steps can reproduce the bug?

1. Configure otel section in config.toml
2. Switch model to gpt-5.5 and reasoning to high
3. Test a prompt with Codex CLI
4. Check Otel logs and you won't see the reasoning as an attribute

What is the expected behavior?

_No response_

Additional information

_No response_