Fix execution history projections and persist live usage

[SaladDay]

Execution history reads and live streams could disagree on supported root/child resources, while Codex kept observed token usage in memory until completion. Share client projections across reads and SSE, and publish current-Turn cumulative usage through the existing durable Runtime path so known measurements survive interruption without double counting.

Preserve native measurement and child-publication limits: unavailable complete usage remains null, and recovery uses public queries rather than SSE replay. Update the contract notes and correct invalid historical function-result fixtures.

Validation:

• Standalone make check covered by server make -o check-web check and local make check-web; SQL generation matched.
• Codex package race tests; 286 client tests, 573 Core Web tests, 74 Playwright tests.
• Real Codex/Kimi, Claude/Kimi and MiniMax Code/M2.7: child/history reads, paging, SDK/raw/TS agreement, live coordination events, disconnect/query recovery, tenant denial and idle Core restart. Codex active measured usage retained after cancellation.
• Fresh independent GPT-6 Astra high whole-diff blind review: no actionable findings; independent client tests and targeted Codex race tests passed.
• Integrated latest main57069ad; related Runtime scan/initialization/recovery/usage PostgreSQL tests passed (12.646s).
• Bounded official Agents API probe with pinned SDK 3.13.0 and two real text Turns, including delayed nullable usage and live-only reconnection.

Limits: Claude/MiniMax complete public token breakdown stays unqualified; Claude child Turn SSE timing differed between attempts; no continuous child progress is claimed. Idle real restart does not qualify active native crash recovery. E2B/product flows were not rerun. Full protocol compatibility is not claimed.