Currently we use execution-date when generating the command to send via executor in https://github.com/apache/airflow/blob/9c94b72d440b18a9e42123d20d48b951712038f9/airflow/models/taskinstance.py#L420-L436

We should replace the execution_date in their to run_id instead and handle the corresponding changes needs on the executor and worker.
airflow/models/taskinstance.py
if use_default:
            jinja_context = {'ti': self}
            
            
            jinja_context.update(
                dict(
                    exception=exception,
                    exception_html=exception_html,
                    try_number=self.try_number - 1,
                    max_tries=self.max_tries,
                )
            )
            jinja_env = jinja2.Environment(
                loader=jinja2.FileSystemLoader(os.path.dirname(__file__)), autoescape=True
            )
            subject = jinja_env.from_string(default_subject).render(**jinja_context)
            html_content = jinja_env.from_string(default_html_content).render(**jinja_context)
            html_content_err = jinja_env.from_string(default_html_content_err).render(**jinja_context)
        else:
            jinja_context = self.get_template_context()
            jinja_context.update(
                dict(
                    exception=exception,
                    exception_html=exception_html,
                    try_number=self.try_number - 1,
                    max_tries=self.max_tries,
                )
            )
            jinja_env = self.task.get_template_env()
            def render(key, content):