let's add a test to make sure this error is throw as expected

Is this test actually doing anything? Is it like you are throwing an TenantIdValidationError in the test and assert the same error is thrown? Ideally we should just invoke the function with the condition (tenancy function without tenant ID, or non-tenant function with tenant ID) and assert the error. You should not use invoke_mock.side_effect directly. Or it's like the test is testing itself

This test is specifically testing error handling, not validation logic.

The actual tenant-id validation logic is already tested in tests/unit/commands/local/lib/test_local_lambda.py in the TestLocalLambda_tenant_id_validation class, which includes:
• test_multi_tenant_function_without_tenant_id_raises_error
• test_non_multi_tenant_function_with_tenant_id_raises_error
• test_multi_tenant_function_with_tenant_id_succeeds
(https://github.com/aws/aws-sam-cli/blob/develop/tests/unit/commands/local/lib/test_local_lambda.py#L1006)
Those tests properly invoke functions with real configurations and let the actual validation logic run.

For the API Gateway service test, the responsibility is different - it needs to verify that when TenantIdValidationError is raised (from the lambda runner), the API Gateway service correctly:

1. Catches the exception
2. Converts it to an HTTP 400 response
3. Returns the proper error message in JSON format