fix: Suppress telemetry emitted inside of BatchLogProcessor::emit (#3172)

Author: lucamuscat

opentelemetry-appender-tracing/tests/test_no_stack_overflow_after_shutdown.rs

@@ -0,0 +1,23 @@
+use opentelemetry_appender_tracing::layer;
+use opentelemetry_sdk::logs::SdkLoggerProvider;
+use tracing::info;
+use tracing_subscriber::{layer::SubscriberExt, util::SubscriberInitExt};
+
+#[test]
+fn test_logging_after_shutdown_does_not_cause_telemetry_induced_telemetry() {
+    //! Reproduces [#3161](https://github.com/open-telemetry/opentelemetry-rust/issues/3161)
+    let exporter = opentelemetry_stdout::LogExporter::default();
+    let provider: SdkLoggerProvider = SdkLoggerProvider::builder()
+        .with_batch_exporter(exporter)
+        .build();
+
+    let otel_layer = layer::OpenTelemetryTracingBridge::new(&provider);
+
+    tracing_subscriber::registry().with(otel_layer).init();
+
+    provider.shutdown().unwrap();
+
+    // If logging causes telemetry-induced-telemetry after shutting down the provider, then a stack
+    // overflow may occur.
+    info!("Don't crash")
+}

opentelemetry-sdk/src/logs/batch_log_processor.rs

@@ -207,6 +207,10 @@ impl LogProcessor for BatchLogProcessor {
                 }
             }
             Err(mpsc::TrySendError::Disconnected(_)) => {
+                // The following `otel_warn!` may cause an infinite feedback loop of
+                // 'telemetry-induced-telemetry', potentially causing a stack overflow
+                let _guard = Context::enter_telemetry_suppressed_scope();
+
                 // Given background thread is the only receiver, and it's
                 // disconnected, it indicates the thread is shutdown
                 otel_warn!(