Bug

When the Anthropic API returns an "out of extra usage" error (Claude usage limit reached), the failover system classifies it as reason=format instead of reason=billing, resulting in a 30-second transient cooldown instead of the intended billing backoff.

Root cause

Anthropic returns this error as:

• HTTP 400 (not 402)
• Error type: invalid_request_error
• Message: "You're out of extra usage. Add more at claude.ai/settings/usage and keep going."

This bypasses both detection layers:

1. HTTP status classification (classifyFailoverReasonFromHttpStatus): status 400 is not 402, so no billing classification from status code.
2. Message classification (isBillingErrorMessage / classifyFailoverClassificationFromMessage): the phrase "out of extra usage" does not match any existing billing pattern ("credit balance", "insufficient credits", "payment required", "plans & billing", etc.).

For 400/422, the code falls back to reason=format when messageClassification is null.

Observed behavior

From gateway logs:

[agent/embedded] embedded run agent end: isError=true model=claude-opus-4-6 provider=anthropic
  error=LLM request rejected: You're out of extra usage. Add more at claude.ai/settings/usage and keep going.
  rawError=400 {"type":"error","error":{"type":"invalid_request_error","message":"You're out of extra usage. Add more at claude.ai/settings/usage and keep going."},"request_id":"sha256:68307bd0318c"}

[model-fallback/decision] model fallback decision:
  decision=candidate_failed requested=anthropic/claude-opus-4-6
  candidate=anthropic/claude-opus-4-6 reason=format next=openrouter/openrouter/auto

Note reason=format — should be reason=billing.

Expected behavior

The error should be classified as reason=billing, triggering the billing cooldown backoff (5h base with exponential backoff) rather than the 30-second transient cooldown.

Suggested fix

Add a pattern to ERROR_PATTERNS.billing in src/agents/pi-embedded-helpers/failover-matches.ts:

billing: [
  // ... existing patterns ...
  /out of (?:extra )?usage/i,
],

Alternatively or additionally, a more specific pattern:

/add more at.*settings\/usage/i,