fix(bash-timeout): native Anthropic bash exception + mutation-proof the detach gate

[code-yeongyu]

Summary

Follow-up to #422, fixing two real defects that post-merge review found. Both were confirmed against merged main before changing anything.

1. Native Anthropic bash advertised a ceiling it could not honor

When PI_ANTHROPIC_BASH is enabled for an anthropic-messages model, the provider replaces the PTY bash tool and the terminal extension steps aside (shouldStepAside). Nothing then implements the cache-deadline auto-detach — but bash-timeout still capped the recommended maximum and told the model a still-running command would be handed to a background session. That promised behavior that could not happen.

The budget is now suppressed on that path, restoring the byte-identical legacy policy. Failing test captured first, then fixed.

Also addressed from the same review:

• the cache-aware prompt now steers cleanup through kill_bash (detached sessions stay live, so the model needs to be told to reap them)
• docs/settings.md documents promptCache.cacheAwareTimeouts and promptCache.safetyBufferSeconds
• builtin/bash-timeout/changes.md added, recording the fork surface and why the exception exists

2. The detach linearization gate had tautological coverage

#422's auto-detach suite had 9 green tests but could not fail for the property it protected: deleting both the queueMicrotask deferral and the settled-aware onExit gate from foreground-detach.ts left all 9 passing.

Root cause: those tests register the exit/abort timers during spawn — before the detach timer exists — so they only exercise "exit was already ordered ahead of D", never the real window between the deadline firing and the queued linearization microtask committing.

test/suite/terminal-detach-gate.test.ts drives createForegroundDetachGate directly with fake timers, so the deadline can fire without yielding the microtask queue:

• exit inside the linearization window → no detach, abort listener untouched
• exit already settled before the deadline → no detach
• abort inside the linearization window → no detach
• still running → detaches exactly once, abort listener removed exactly once
• onExit dispatching synchronously at registration → exit stays authoritative (covers exitedAtGate)
• cancel() → suppresses a pending detach

Mutation proof

Mutation	Result
remove queueMicrotask(linearize) deferral	2 tests fail
remove the settled-aware onExit gate	1 test fails
unmodified	6/6 pass

The gate itself was correct — it was simply unprotected.

Verification

npm run check exit 0. Focused suites 65/65 (bash-timeout-extension, bash-timeout-handlers, terminal-detach-gate, terminal-bash-auto-detach, prompt-surface-stale-wait-idioms, prompt-cache-budget).