Expose current runtime model display name to Codex sessions

Feature request

Expose the exact current runtime model/profile metadata to Codex sessions as read-only context.

Problem

Codex can currently infer broad identity from system context, such as being based on GPT-5, but it cannot reliably access the exact model/profile label shown in the client UI. For example, the UI may show a label like gpt-5.5 xhigh, while the assistant only knows a broad family name.

This creates friction for workflows that need accurate provenance, including:

• commit co-author trailers
• PR descriptions and handoff notes
• audit logs
• debugging reports
• reproducibility metadata

In one practical case, the assistant was asked to add a commit trailer using the current model name. It first used a placeholder, then a broad family name, because the exact UI model/profile label was not available to the assistant.

Suggested behavior

Provide a read-only runtime metadata field in the assistant/session context, for example:

• model_id: stable API/internal model identifier
• model_display_name: exact client UI label
• reasoning_profile or equivalent: e.g. effort/profile/tier when applicable

The assistant should be able to reference these values when the user explicitly asks for model provenance or generated metadata.

Why this helps

This would avoid guesswork and make generated commit trailers, PR metadata, audit notes, and debugging reports more accurate. Claude-like tooling appears to expose the active model name more directly, and having equivalent metadata in Codex would improve developer workflows.