feat(web): show thread API cost in composer

[saphid]

What changed

The web composer shows the active thread public-list API cost beside the send button. Hovering or clicking opens the cache-write, cache-read, fresh input plus output, and provider-reported breakdown. Sub-cent totals retain useful precision.

The server now keeps the final progressive Claude response snapshot, expands fallback attempts, preserves separate 5-minute and 1-hour cache-write counters, and falls back to the top-level serving model when an iteration omits its own model. The scan-cache version advances so previously cached false-zero Claude records are discarded and rebuilt.

Pricing now honors LiteLLM context-length tiers from each request total input, including the GPT-5.6 Sol tier above 272k tokens. Service tiers such as priority, flex, and batch remain at base public-list rates because local transcripts do not identify them.

Why the displayed value was wrong

The composer arithmetic and formatting were not the cause. The combined accounting parser required every Claude iteration to repeat its model even though real Claude transcripts commonly place the serving model only on the parent message. It therefore dropped billed iterations before thread attribution and handed the UI zeros.

A read-only audit of the affected real session found 857 of 871 usage-bearing lines in that shape. The broken path retained 14 deduplicated records containing zero tokens; the corrected path retains 369 records containing 109,779,332 billed tokens.

A separate pricing audit found 96 cached GPT-5.6 Sol requests above 272k input. Base-only pricing produced $18.953256; the published long-context tier produces $37.390112, a prior understatement of $18.436856.

Stack note

This remains stacked on #9 because that PR adds the cache-write component used by the composer. The current head of #28 still contains the model-less-iteration defect, so this PR carries the corrected accounting rather than depending on that broken head.

Surfaces

• Web and desktop: corrected composer cost and existing Usage page.
• React Native mobile: corrected shared usage totals and clearer estimate/cache-write wording.
• SwiftUI mobile: no Usage or composer-cost surface exists, so no native change applies.
• Providers: Claude parsing and OpenAI/Codex long-context pricing change; Grok parsing is unchanged.
• Local, remote, and tunnel clients receive the same versioned summary and thread-breakdown contract.

Verification

• 119 focused server usage tests passed.
• 51 focused web and shared usage tests passed.
• Contracts, server, web, and React Native mobile typechecks passed.
• Targeted lint passed with four pre-existing React ref warnings in UsagePage.
• All 17 changed files pass formatting and git diff checks.
• The real-session parser audit and cached long-context pricing audit reproduced the corrections above without reading or printing message content.

Checklist

• The value is derived from transcript records attributed to every retained provider session.
• Progressive snapshots, fallback attempts, model-less iterations, and cache TTLs are covered.
• Component costs reconcile with the headline total.
• Old false-zero scan-cache entries are invalidated.
• Applicable long-context public-list tiers are selected from recorded input totals.
• No animation or composer layout change was added.

Built by gpt-5.6-sol in T3 Code through the Codex harness.