### Check for existing issues

- [x] I have searched the existing issues and checked that my issue is not a duplicate.

### What happened?

When Claude Code is configured to route through a LiteLLM proxy using claude.ai OAuth passthrough (anthropic-beta: oauth-2025-04-20), auto mode fires a separate classifier HTTP call before every Bash command to determine safety. This classifier call hits the same claude.ai subscription rate-limit pool as the main conversation turn, doubling the request volume per Bash command.

Under moderate load, the classifier call returns 429 rate_limit_error. Claude Code then hard-blocks the Bash tool entirely with:

"claude-sonnet-4-6-oauth is temporarily unavailable, so auto mode cannot determine the safety of Bash right now."

Non-Bash tools (file reads, edits, etc.) are unaffected. The failure is intermittent — the same session can succeed then fail depending on how many classifier calls have fired recently.

Expected: Classifier 429 should either be retried transparently, or fall back to a lighter model, rather than hard-blocking the tool call.

### Steps to Reproduce

Deploy LiteLLM proxy with an OAuth-passthrough alias (e.g. claude-sonnet-4-6-oauth)…