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,
        mark_success: bool = False,
        test_mode: bool = False,
        job_id: Optional[str] = None,
        pool: Optional[str] = None,
        error_file: Optional[str] = None,
        session=None,
    ) -> None:
        """
        Immediately runs the task (without checking or changing db state
        before execution) and then sets the appropriate final state after
        completion and runs any post-execute callbacks. Meant to be called
        only after another function changes the state to running.
        :param mark_success: Don't run the task, mark its state as success
        :type mark_success: bool
        :param test_mode: Doesn't record success or failure in the DB
        :type test_mode: bool
        :param pool: specifies the pool to use to run the task instance
        :type pool: str
        :param session: SQLAlchemy ORM Session
        :type session: Session
        """
        task = self.task
        self.test_mode = test_mode
        self.refresh_from_task(task, pool_override=pool)
        self.refresh_from_db(session=session)
        self.job_id = job_id