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
"""
        Returns whether or not all the conditions are met for this task instance to be run
        given the context for the dependencies (e.g. a task instance being force run from
        the UI will ignore some dependencies).
        :param dep_context: The execution context that determines the dependencies that
            should be evaluated.
        :type dep_context: DepContext
        :param session: database session
        :type session: sqlalchemy.orm.session.Session
        :param verbose: whether log details on failed dependencies on
            info or debug log level
        :type verbose: bool
        """
        dep_context = dep_context or DepContext()
        failed = False
        verbose_aware_logger = self.log.info if verbose else self.log.debug
        for dep_status in self.get_failed_dep_statuses(dep_context=dep_context, session=session):
            failed = True
            verbose_aware_logger(
                "Dependencies not met for %s, dependency '%s' FAILED: %s",
                self,
                dep_status.dep_name,
                dep_status.reason,
            )
        if failed:
            return False
        verbose_aware_logger("Dependencies all met for %s", self)
        return True
    @provide_session
    def get_failed_dep_statuses(self, dep_context=None, session=None):