### 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)

"""
        Called for [Operator] > [Outlet], so that if other is an attr annotated object
        it is set as an outlet of this Operator.
        """
        if not isinstance(other, Iterable):
            other = [other]
        for obj in other:
            if not attr.has(obj):
                raise TypeError(f"Left hand side ({obj}) is not an outlet")
        self.add_outlets(other)
        return self
    def __lt__(self, other):
        """
        Called for [Inlet] > [Operator] or [Operator] < [Inlet], so that if other is
        an attr annotated object it is set as an inlet to this operator
        """
        if not isinstance(other, Iterable):
            other = [other]
        for obj in other:
            if not attr.has(obj):
                raise TypeError(f"{obj} cannot be an inlet")
        self.add_inlets(other)
        return self
    def __setattr__(self, key, value):