https://github.com/open-telemetry/opentelemetry-rust/blob/main/opentelemetry-otlp/src/exporter/tonic/metrics.rs#L58

Tonic MetricExporter uses std::Mutex to protect inner client, and the lock is held across await points. This can cause deadlock. The fix would be to use tokio::Mutex, but then shutdown/cleanup cannot be easily done, like already faced by LogExporter. But that is better than having code that deadlocks.

Opening an issue to track fixing this.