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
"""
            Wrapper around Variable. This way you can get variables in
            templates by using ``{{ var.json.variable_name }}`` or
            ``{{ var.json.get('variable_name', {'fall': 'back'}) }}``.
            """
            def __init__(self):
                self.var = None
            def __getattr__(
                self,
                item: str,
            ):
                self.var = Variable.get(item, deserialize_json=True)
                return self.var
            def __repr__(self):
                return str(self.var)
            @staticmethod
            def get(
                item: str,
                default_var: Any = Variable._Variable__NO_DEFAULT_SENTINEL,
            ):
                """Get Airflow Variable after deserializing JSON value"""
                return Variable.get(item, default_var=default_var, deserialize_json=True)
        class ConnectionAccessor:
            """
            Wrapper around Connection. This way you can get connections in
            templates by using ``{{ conn.conn_id }}`` or
            ``{{ conn.get('conn_id') }}``.
            """
            def __getattr__(