feat(web): show Claude round usage metadata

[junmo-kim]

Summary

This follows up on #637, which aggregated per-message metadata across a response group. Claude's final SDK result now lets the same surface show authoritative round-level usage, cost, duration, and turn count instead of deriving them from individual messages.

• preserve the Claude Agent SDK's final result as authoritative metadata for the preceding response round
• show models, processed tokens, cache-read share, API-rate estimate, elapsed round time, and internal turns in the message-details popover
• keep existing metadata labels unchanged when a round result is unavailable

Details

Claude assistant messages expose per-message usage, while the SDK's final result contains the complete round-level usage, per-model breakdown, cost, duration, and turn count. The CLI now forwards that result through the existing system/turn_duration carrier without advancing the main or sidechain parent chain. The remote queue preserves visible system carriers and drains them before ready, while Web reconciliation retains late-arriving round summaries. The web app validates it at the normalization boundary, attaches it to the preceding contiguous assistant response group, and prefers it over derived per-message aggregates.

Malformed counters fail closed. Token and turn counts require non-negative safe integers, cost and duration require finite non-negative numbers, and a zero cost is omitted rather than presented as free usage.

Test plan

• full CLI Vitest suite (2,439 passed, 1 skipped)
• full Hub suite (1,205 passed, 3 skipped)
• full Web Vitest suite (2,842 passed)
• full Shared and Relay suites (294 and 80 passed)
• CLI and Web typechecks
• Web production build
• isolated Hub + Vite + real Claude Haiku request + Playwright verification on desktop and iPhone 13, without a page reload

Screenshots

Desktop	Mobile

[github-actions]

Findings

• No findings.

Summary
Review mode: initial

No issues meeting the ≥80% confidence threshold were found in the added or modified lines. Residual risk: the change spans CLI message ordering and Web normalization/reconciliation, so correctness still depends on the full automated suite and representative Claude SDK result shapes.

Testing

• Not run (automation); static review only. The diff adds coverage for result conversion, queue ordering, malformed-counter normalization, sidechain attachment, late reconciliation, tool-only grouping, and metadata formatting.

HAPI Bot