Improve cross-provider dependency detection (apache#45784)

When another provider is only used in example dags, we should not
make it "cross-provider" dependency - this happened to "edge" provider
having "common.compat" as cross-provider dependency.

It has been previously only implemented for "standard" provider but
this is a universal rule that could be applied to any other provider.

generated/provider_dependencies.json

@@ -535,9 +535,7 @@
         "plugin-class": "airflow.providers.edge.plugins.edge_executor_plugin.EdgeExecutorPlugin"
       }
     ],
-    "cross-providers-deps": [
-      "common.compat"
-    ],
+    "cross-providers-deps": [],
     "excluded-python-versions": [],
     "state": "not-ready"
   },

scripts/ci/pre_commit/update_providers_dependencies.py

@@ -206,11 +206,15 @@ def check_if_different_provider_used(file_path: Path) -> None:
             warnings.append(f"The provider {imported_provider} from {file_path} cannot be found.")
             continue
 
-        if imported_provider == "standard":
-            # Standard -- i.e. BashOperator is used in a lot of example dags, but we don't want to mark this
+        if "/example_dags/" in file_path.as_posix():
+            # If provider is used in a example dags, we don't want to mark this
             # as a provider cross dependency
-            if file_path.name == "celery_executor_utils.py" or "/example_dags/" in file_path.as_posix():
-                continue
+            continue
+        if imported_provider == "standard" and file_path.name == "celery_executor_utils.py":
+            # some common standard operators are pre-imported in celery when it starts in order to speed
+            # up the task startup time - but it does not mean that standard provider is a cross-provider
+            # dependency of the celery executor
+            continue
         if imported_provider:
             if file_provider != imported_provider:
                 ALL_DEPENDENCIES[file_provider]["cross-providers-deps"].append(imported_provider)