Skip example importability tests for providers in non-main branches (a…

…pache#43260)

When "Always" tests are running in v2* branches, they also tested
provider examples for importability. However sometimes those tests
failed because we have not cherry-picked some of the provider's
changes that were necessary for the examples to get imported.

This PR excludes provider's examples from the "always" running
importability tests, when the branch we are running it in is
not main (i.e. we are in one of the past v2-branches).

tests/always/test_example_dags.py

@@ -115,6 +115,7 @@ def get_python_excluded_providers_folders() -> list[str]:
 
 def example_not_excluded_dags(xfail_db_exception: bool = False):
     example_dirs = ["airflow/**/example_dags/example_*.py", "tests/system/**/example_*.py"]
+
     suspended_providers_folders = get_suspended_providers_folders()
     current_python_excluded_providers_folders = get_python_excluded_providers_folders()
     suspended_providers_folders = [
@@ -129,7 +130,13 @@ def example_not_excluded_dags(xfail_db_exception: bool = False):
     ]
     providers_folders = tuple([AIRFLOW_SOURCES_ROOT.joinpath(pp).as_posix() for pp in PROVIDERS_PREFIXES])
 
+    default_branch = os.environ.get("DEFAULT_BRANCH", "main")
+    include_providers = default_branch == "main"
+
     for example_dir in example_dirs:
+        if not include_providers and "providers/" in example_dir:
+            print(f"Skipping {example_dir} because providers are not included for {default_branch} branch.")
+            continue
         candidates = glob(f"{AIRFLOW_SOURCES_ROOT.as_posix()}/{example_dir}", recursive=True)
         for candidate in sorted(candidates):
             param_marks = []