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
"""Fetch rendered template fields from DB"""
        from airflow.models.renderedtifields import RenderedTaskInstanceFields
        rendered_task_instance_fields = RenderedTaskInstanceFields.get_templated_fields(self)
        if rendered_task_instance_fields:
            for field_name, rendered_value in rendered_task_instance_fields.items():
                setattr(self.task, field_name, rendered_value)
        else:
            try:
                self.render_templates()
            except (TemplateAssertionError, UndefinedError) as e:
                raise AirflowException(
                    "Webserver does not have access to User-defined Macros or Filters "
                    "when Dag Serialization is enabled. Hence for the task that have not yet "
                    "started running, please use 'airflow tasks render' for debugging the "
                    "rendering of template_fields."
                ) from e
    @provide_session
    def get_rendered_k8s_spec(self, session=None):
        """Fetch rendered template fields from DB"""
        from airflow.models.renderedtifields import RenderedTaskInstanceFields
        rendered_k8s_spec = RenderedTaskInstanceFields.get_k8s_pod_yaml(self, session=session)
        if not rendered_k8s_spec:
            try:
                rendered_k8s_spec = self.render_k8s_pod_yaml()
            except (TemplateAssertionError, UndefinedError) as e:
                raise AirflowException(f"Unable to render a k8s spec for this taskinstance: {e}") from e
        return rendered_k8s_spec
    def overwrite_params_with_dag_run_conf(self, params, dag_run):