### Check for existing issues

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

### What happened?

When using Claude Code via LiteLLM proxy with Bedrock InvokeModel (`bedrock/` prefix), requests containing `context_management` (compaction) fail with:

``` {"message":"context_management: Extra inputs are not permitted"} ```

The root cause: LiteLLM's `/v1/messages` endpoint passes `context_management` through to Bedrock InvokeModel, but does **not** inject the required `compact-2026-01-12` beta header into the request body's `anthropic_beta` array.

Bedrock InvokeModel requires `"anthropic_beta": ["compact-2026-01-12"]` in the request body when `context_management` is present. Without it, Bedrock rejects the request.

## Key findings

1. Bedrock InvokeModel **does support** compaction — verified by direct HTTP call with `Authorization: Bearer` API key 2. The `anthropic_beta_headers_config.json` already has `"compact-2026-01-12": "compact-2026-01-12"` for the `bedrock` provider 3. However, `get_anthropic_beta_list()` in `litellm/llms/anthropic/common_utils.py` does NOT detect `context_management` and does NOT auto-inject `compact-2026-01-12` 4…