### 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)

return not self == other
    def __hash__(self):
        hash_components = [type(self)]
        for component in self._comps:
            val = getattr(self, component, None)
            try:
                hash(val)
                hash_components.append(val)
            except TypeError:
                hash_components.append(repr(val))
        return hash(tuple(hash_components))
    
    def __or__(self, other):
        """
        Called for [This Operator] | [Operator], The inlets of other
        will be set to pick up the outlets from this operator. Other will
        be set as a downstream task of this operator.
        """
        if isinstance(other, BaseOperator):
            if not self.outlets and not self.supports_lineage:
                raise ValueError("No outlets defined for this operator")
            other.add_inlets([self.task_id])
            self.set_downstream(other)
        else:
            raise TypeError(f"Right hand side ({other}) is not an Operator")
        return self
    
    def __gt__(self, other):