[codex] Clarify Anthropic extra-usage exhaustion errors

[HiddenPuppy]

Summary

• detect Anthropic's "You're out of extra usage" API error separately from generic non-retryable 400s
• surface clearer guidance that this is a third-party/Hermes API usage limit, not something restart or re-login usually fixes
• return actionable next steps to CLI and gateway users, and cover the behavior with a regression test

Root Cause

Hermes treated Anthropic's extra-usage exhaustion response like any other non-retryable client error. The request failure itself was correct, but the messaging was too generic, which made a usage-limit state look like a broken login or Hermes bug.

Validation

• ran pytest -n 0 tests/run_agent/test_anthropic_error_handling.py
• result: 9 passed in 90.30s
• ran pytest -n 0 tests/run_agent/test_long_context_tier_429.py
• result: 15 passed in 0.14s

Fixes #6475

[alt-glitch]

Related to #11736, #13170 — same Anthropic 'out of extra usage' classification issue.

[alt-glitch]

Related to #11736, #13170 — same Anthropic 'out of extra usage' classification issue.

[OutThisLife]

Thanks @HiddenPuppy — closing as implemented on main.

The core of this PR — detecting Anthropic's "out of extra usage" 400 as a billing/entitlement condition (instead of an opaque non-retryable error) and surfacing actionable guidance — has since landed via #56128 (merged 2026-07-01):

• agent/error_classifier.py now lists "out of extra usage" in _BILLING_PATTERNS, so the 400 classifies as FailoverReason.billing (rotate + fallback) rather than format_error.
• agent/conversation_loop.py _billing_or_entitlement_message has a dedicated Anthropic branch that points at https://claude.ai/settings/usage, notes the billing-cycle reset, and offers the /model … --provider … switch — the same actionable next-steps this PR added, via the canonical CLI + gateway guidance path.

One thing #56128 does not cover, and this PR didn't either: the sibling phrasing "Third-party apps now draw from your extra usage / enable extra usage" (a distinct 400 body). That's addressed in #49379, which is staying open.

Appreciate the report and the fix — the behavior you were after is now the default.