### Apache Airflow version

main (development)

### What happened

When creating a DAG with Task Groups and a Mapped Operator, if the Task Group is passed as argument to Mapped Operator's `partial` method it is ignored and the operator is not added to the group.

### What you think should happen instead

The Mapped Operator should be added to the Task Group passed as an argument.

### How to reproduce

Create a DAG with a source code like the following one

```python
from airflow import DAG
from airflow.operators.bash import BashOperator
from airflow.operators.empty import EmptyOperator
from airflow.utils import timezone
from airflow.utils.task_group import TaskGroup


with DAG("dag", start_date=timezone.datetime(2016, 1, 1)) as dag:
    start = EmptyOperator(task_id="start")
    finish = EmptyOperator(task_id="finish")

    group = TaskGroup("test-group")
    commands = ["echo a", "echo b", "echo c"]
    mapped = BashOperator.partial(task_id="task_2", task_group=group).expand(bash_command=commands)

    start >> group >> finish

# assert mapped.task_group == group

```

### Operating System

macOS 13.2.1 (22D68)

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other

### Deployment details

_No response_

### Anything else

_No response_

### Are you willing to submit PR?

- [X] Yes I am willing to submit a PR!

### Code of Conduct

- [X] I agree to follow this project's [Code of Conduct](https://github.com/apache/airflow/blob/main/CODE_OF_CONDUCT.md)

"""Returns True if the Operator has been assigned to a DAG."""
        return self._dag is not None
    deps: frozenset[BaseTIDep] = frozenset(
        {
            NotInRetryPeriodDep(),
            PrevDagrunDep(),
            TriggerRuleDep(),
            NotPreviouslySkippedDep(),
        }
    )
    """
    Returns the set of dependencies for the operator. These differ from execution
    context dependencies in that they are specific to tasks and can be
    extended/overridden by subclasses.
    """
    def prepare_for_execution(self) -> BaseOperator:
        """
        Lock task for execution to disable custom action in __setattr__ and
        returns a copy of the task
        """
        other = copy.copy(self)
        other._lock_for_execution = True
        return other
    def set_xcomargs_dependencies(self) -> None: