some fixes

Author: alibeyram

pydantic_ai_slim/pydantic_ai/_tool_manager.py

@@ -106,6 +106,11 @@ async def handle_call(
         """
         if self.tools is None or self.ctx is None:
             raise ValueError('ToolManager has not been prepared for a run step yet')  # pragma: no cover
+        
+        if (tool := self.tools.get(call.tool_name)) and tool.tool_def.kind == 'output':
+            output_tool_flag = True
+        else:
+            output_tool_flag = False
 
         return await self._call_function_tool(
                 call,
@@ -116,6 +121,7 @@ async def handle_call(
                 include_content=self.ctx.trace_include_content,
                 instrumentation_version=self.ctx.instrumentation_version,
                 usage=self.ctx.usage,
+                output_tool_flag=output_tool_flag,
             )
 
     async def _call_tool(
@@ -204,16 +210,17 @@ async def _call_function_tool(
         include_content: bool,
         instrumentation_version: int,
         usage: RunUsage,
+        output_tool_flag: bool = False,
     ) -> Any:
         """See <https://opentelemetry.io/docs/specs/semconv/gen-ai/gen-ai-spans/#execute-tool-span>."""
         instrumentation_names = InstrumentationNames.for_version(instrumentation_version)
 
-        if (tool := self.tools.get(call.tool_name)) and tool.tool_def.kind == 'output':
-            tool_name: str = 'Output Tool'
-            output_tool_flag = True
+        if output_tool_flag:
+            tool_name = 'output tool'
         else:
-            tool_name: str = call.tool_name
-            output_tool_flag = False
+            tool_name = call.tool_name
+
+
 
         span_attributes = {
             'gen_ai.tool.name': tool_name,