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
self,
        state: Optional[str] = None,
        session: Optional[Session] = None,
    ) -> Optional["DagRun"]:
        """The DagRun that ran before this task instance's DagRun.
        :param state: If passed, it only take into account instances of a specific state.
        :param session: SQLAlchemy ORM Session.
        """
        dag = self.task.dag
        if dag is None:
            return None