Expose the client surface (GUI/desktop vs TUI vs IDE) to the model

What
The model has no signal in its session context indicating which Claude Code client the user is on — desktop/web GUI, terminal TUI, or IDE extension.

Why it matters
The assistant hands out surface-specific instructions that don't apply. Example: when asked how to end a session, it suggested /exit, Ctrl+C, and Ctrl+D — all TUI-only. On the GUI those don't exist, so the guidance was wrong until I told it I was on the GUI.

Suggestion
Include the client surface in the environment/system context so responses can be tailored (e.g. session lifecycle, keyboard shortcuts, available slash commands).