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: Session = None
    ) -> Optional[pendulum.DateTime]:
        """
        The start date from property previous_ti_success.
        :param state: If passed, it only take into account instances of a specific state.
        :param session: SQLAlchemy ORM Session
        """
        self.log.debug("previous_start_date was called")
        prev_ti = self.get_previous_ti(state=state, session=session)
        
        return prev_ti and prev_ti.start_date and pendulum.instance(prev_ti.start_date)
    @property
    def previous_start_date_success(self) -> Optional[pendulum.DateTime]:
        """
        This attribute is deprecated.
        Please use `airflow.models.taskinstance.TaskInstance.get_previous_start_date` method.
        """
        warnings.warn(
            """
            This attribute is deprecated.
            Please use `airflow.models.taskinstance.TaskInstance.get_previous_start_date` method.
            """,
            DeprecationWarning,
            stacklevel=2,
        )
        return self.get_previous_start_date(state=State.SUCCESS)
    @provide_session
    def are_dependencies_met(self, dep_context=None, session=None, verbose=False):