[FEATURE] Higher time resolution (seconds) + timezone display for completion line ("Brewed for Xs · done H:MM AM/PM")

Summary

The end-of-turn completion line (e.g. "Brewed for 23s · done 8:54 PM") only shows whole-second granularity on elapsed time and no timezone indicator on the wall-clock timestamp. Requesting more resolution on both, ideally as the default.

Request

1. Increase default time resolution:

• Elapsed duration ("Brewed for 23s") → show sub-second precision (e.g. "23.4s") when useful, or at minimum keep whole seconds but ensure it's not truncated/rounded in a way that hides real duration.
• Wall-clock timestamp ("done 8:54 PM") → include timezone (e.g. "8:54:12 PM PDT").

1. If not made default, expose a user-customizable setting (similar in spirit to the existing "Time format" config option — auto / 12-hour / 24-hour / 24-hour-utc) that adds:

• Seconds in the wall-clock timestamp
• The local timezone abbreviation or offset

Motivation

The current "Time format" setting (auto/12-hour/24-hour/24-hour-utc) only toggles 12h vs 24h display — it doesn't add seconds or show which timezone is in effect. Users working across timezones or wanting more precise timing feedback have no way to get this without a change to the harness.

Related

• #52420 (customizable completion-line verbs — different axis of customization, same UI element)
• #84796 (spinner elapsed time should track total time since prompt — different metric, same area)

Environment

Claude Code CLI, macOS