Include structured retry exhaustion accounting and correlation IDs in terminal failures

[danielkov]

Summary

Terminal provider failures do not expose a complete structured retry summary. Attempt count can appear in rendered text and fatal records already have session/event identity, but cumulative backoff and correlation data are not propagated together as typed exhaustion metadata to the failing tool boundary.

Split from #35 after the transient overload retry policy was fixed by #32.

Desired behavior

On retry exhaustion, provide a structured, sanitized summary containing:

• total attempts;
• cumulative backoff or sleep time;
• total elapsed retry time;
• final retry/exhaustion category; and
• session ID and event ID, or an equivalent stable correlation reference to the fatal record.

The parent should not need to parse a rendered error string or search ~/.kit/errors to correlate the tool failure with its fatal record. This issue is about terminal accounting; live progress belongs in a separate issue.

Suggested coverage

• Use deterministic time to verify attempts, cumulative delays, and elapsed time.
• Verify the parent-visible structured failure correlates with the schema-v2 fatal record.
• Cover subagent(...) through compose(background=true).
• Assert no provider body, credentials, private prompts, or customer identifiers are exposed.

Environment

• Originally observed with Kit 0.1.96 on Darwin 25.6.0 arm64.
• Confirmed as a remaining gap on Kit 0.1.105 on Darwin 25.5.0 arm64.
• Surface: ACP; provider route: openai-subscription.

Related work

• ACP subagents terminate on repeated openai-subscription server overloads #35
• fix(provider): overhaul openai-subscription retry policy #32