How to make a custom action fail to prevent furthur actions from firing?

How To
1

There is a post already asking the question here, but it’s from 2024 and was never answered.

The short story is that I have a newsletter signup form that uses a custom action to make sure the user doesn’t already exist, and isn’t already in the “newsletter” role before making the account and/or assigning the role.
If a user is made or added, a welcome email is added using the “email” action. If a user is already signed up, an error is returned to the form using:

else {
                $result_output = "This address was already subscribed. Please search your inbox for the original welcome email.";
                $result_type = 'error';
            }
        }   

        $form->set_result([
            'action'  => 'my_custom_action',
            'type'    => "$result_type", // 'success', 'error', or 'info'
            'message' => "$result_output",
    ]);

But… the welcome email still sends. How do I communicate to the form that the custom action has failed and I want no further actions triggered?