### 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)

""":meta private:"""
        return self
Chainable = Union[DependencyMixin, Sequence[DependencyMixin]]
def chain(*tasks: DependencyMixin | Sequence[DependencyMixin]) -> None:
    r"""
    Given a number of tasks, builds a dependency chain.
    This function accepts values of BaseOperator (aka tasks), EdgeModifiers (aka Labels), XComArg, TaskGroups,
    or lists containing any mix of these types (or a mix in the same list). If you want to chain between two
    lists you must ensure they have the same length.
    Using classic operators/sensors:
    .. code-block:: python
        chain(t1, [t2, t3], [t4, t5], t6)
    is equivalent to::
          / -> t2 -> t4 \
        t1               -> t6
          \ -> t3 -> t5 /
    .. code-block:: python
        t1.set_downstream(t2)
        t1.set_downstream(t3)
        t2.set_downstream(t4)
        t3.set_downstream(t5)
        t4.set_downstream(t6)
        t5.set_downstream(t6)
    Using task-decorated functions aka XComArgs:
    .. code-block:: python
        chain(x1(), [x2(), x3()], [x4(), x5()], x6())
    is equivalent to::
          / -> x2 -> x4 \
        x1               -> x6