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,
        verbose: bool = True,
        ignore_all_deps: bool = False,
        ignore_depends_on_past: bool = False,
        ignore_task_deps: bool = False,
        ignore_ti_state: bool = False,
        mark_success: bool = False,
        test_mode: bool = False,
        job_id: Optional[str] = None,
        pool: Optional[str] = None,
        session=None,
    ) -> bool:
        """
        Checks dependencies and then sets state to RUNNING if they are met. Returns
        True if and only if state is set to RUNNING, which implies that task should be
        executed, in preparation for _run_raw_task
        :param verbose: whether to turn on more verbose logging
        :type verbose: bool
        :param ignore_all_deps: Ignore all of the non-critical dependencies, just runs
        :type ignore_all_deps: bool