Fix setting otel tracing provider (#1594)

### Purpose
We should use the global otel tracing provider if it's set outside of
LangSmith

Author: angus-langchain

python/langsmith/client.py

@@ -623,10 +623,25 @@ def __init__(
                     "LANGSMITH_OTEL_ENABLED is set but OpenTelemetry packages are not installed. "
                     "Install with `pip install langsmith[otel]`"
                 )
+            existing_provider = otel_trace.get_tracer_provider()
+            tracer = existing_provider.get_tracer(__name__)
             if otel_tracer_provider is None:
-                otel_tracer_provider = get_otlp_tracer_provider()
-            # Set as global tracer provider if we're creating a new one
-            otel_trace.set_tracer_provider(otel_tracer_provider)
+                # Use existing global provider if available
+                if not (
+                    isinstance(existing_provider, otel_trace.ProxyTracerProvider)
+                    and hasattr(tracer, "_tracer")
+                    and isinstance(
+                        cast(
+                            otel_trace.ProxyTracer,
+                            tracer,
+                        )._tracer,
+                        otel_trace.NoOpTracer,
+                    )
+                ):
+                    otel_tracer_provider = cast(TracerProvider, existing_provider)
+                else:
+                    otel_tracer_provider = get_otlp_tracer_provider()
+                    otel_trace.set_tracer_provider(otel_tracer_provider)
 
             self.otel_exporter = OTELExporter(tracer_provider=otel_tracer_provider)