[Core] respect tracing project name cvar (#28792)

libs/core/langchain_core/callbacks/manager.py

@@ -2379,6 +2379,7 @@ def _configure(
                             if run_tree is not None
                             else tracing_context["client"]
                         ),
+                        tags=tracing_tags,
                     )
                     callback_manager.add_handler(handler, True)
                 except Exception as e:

libs/core/langchain_core/tracers/context.py

@@ -13,8 +13,8 @@ from typing import (
 )
 from uuid import UUID
 
+from langsmith import run_helpers as ls_rh
 from langsmith import utils as ls_utils
-from langsmith.run_helpers import get_run_tree_context
 
 from langchain_core.tracers.langchain import LangChainTracer
 from langchain_core.tracers.run_collector import RunCollectorCallbackHandler
@@ -149,7 +149,10 @@ def _tracing_v2_is_enabled() -> Union[bool, Literal["local"]]:
 
 
 def _get_tracer_project() -> str:
-    run_tree = get_run_tree_context()
+    tracing_context = ls_rh.get_tracing_context()
+    run_tree = tracing_context["parent"]
+    if run_tree is None and tracing_context["project_name"] is not None:
+        return tracing_context["project_name"]
     return getattr(
         run_tree,
         "session_name",