### Check for existing issues

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

### What happened?

### Actual behavior

With `LITELLM_OTEL_V2=true`, metadata listed in `callback_settings.otel.baggage_metadata_keys` is missing from the normal proxy LLM-call span when that metadata is available in the final `StandardLoggingPayload` but was not part of the auth-time `UserAPIKeyAuth` object.

This is the common path because OTel v2 opens the LLM span in `log_pre_api_call`. At close, `RequestIdentity.from_payload()` contains the request/routing metadata, but `_close_llm_call()` calls `finish_span()` without applying the configured metadata allowlist. `_seed_identity_baggage()` is only used when span creation was deferred, so the same request can have different metadata depending on whether the span was opened at the boundary.

The configured allowlist therefore does not reliably produce `litellm.metadata.<key>` attributes. This also prevents vendor mappers such as Langfuse from receiving operator-approved late request/routing metadata.

### Expected behavior

Every key explicitly listed in `baggage_metadata_keys` should be stamped on the LLM-call…