### Apache Airflow version

2.2.0 (latest released)

### Operating System

Ubuntu

### Versions of Apache Airflow Providers

_No response_

### Deployment

Other

### Deployment details

Just used `airflow standalone`

### What happened

First:

TaskGroup does not show the tooltip that is defined for that group on hover
![2021-10-19_17h00_18](https://user-images.githubusercontent.com/35238779/137937706-376922b8-2f79-47ac-9789-6007d135f855.png)

Second:

Providing an Operator with `task_group=` instead of TaskGroup as context manager ignores that TaskGroup's default_args. Using the code I provided below, the task "end" in section_3 has the wrong owner.


### What you expected to happen

First:

If a TaskGroup is used and the tooltip is defined like so:
```python
with TaskGroup("section_1", tooltip="Tasks for section_1") as section_1:
```
the information provided with`tooltip="..."` should show on hover, as shown in the official documentation at https://airflow.apache.org/docs/apache-airflow/stable/concepts/dags.html#taskgroups


Second:

Defining a TaskGroup with default_args like
```python
section_3 = TaskGroup("section_3", tooltip="Tasks for section_2", default_args={"owner": "bug"})
```
should result in those default_args being used by tasks defined like so:
```python
end = DummyOperator(task_id="end", task_group=section_3)
```

### How to reproduce

I have tested this with the below code

```python
from datetime import datetime

from airflow.models.dag import DAG
from airflow.operators.bash import BashOperator
from airflow.operators.dummy import DummyOperator
from airflow.utils.task_group import TaskGroup

with DAG(
    dag_id="task_group_test",
    start_date=datetime(2021, 1, 1),
    catchup=False,
    tags=["example"],
    default_args={"owner": "test"},
) as dag:
    start = DummyOperator(task_id="start")

    with TaskGroup("section_1", tooltip="Tasks for section_1") as section_1:
        task_1 = DummyOperator(task_id="task_1")
        task_2 = BashOperator(task_id="task_2", bash_command="echo 1")
        task_3 = DummyOperator(task_id="task_3")

        task_1 >> [task_2, task_3]

    with TaskGroup(
        "section_2", tooltip="Tasks for section_2", default_args={"owner": "overwrite"}
    ) as section_2:
        task_1 = DummyOperator(task_id="task_1")

    section_3 = TaskGroup("section_3", tooltip="Tasks for section_3", default_args={"owner": "bug"})

    end = DummyOperator(task_id="end", task_group=section_3)

    start >> section_1 >> section_2 >> section_3
```

### Anything else

_No response_

### Are you willing to submit PR?

- [ ] 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)

airflow/www/views.py
).join(
            running_dag_run_query_result,
            and_(
                running_dag_run_query_result.c.dag_id == TaskInstance.dag_id,
                running_dag_run_query_result.c.run_id == TaskInstance.run_id,
            ),
        )
        if conf.getboolean('webserver', 'SHOW_RECENT_STATS_FOR_COMPLETED_RUNS', fallback=True):
            last_dag_run = (
                session.query(DagRun.dag_id, sqla.func.max(DagRun.execution_date).label('execution_date'))
                .join(DagModel, DagModel.dag_id == DagRun.dag_id)
                .filter(DagRun.state != State.RUNNING, DagModel.is_active)
                .group_by(DagRun.dag_id)
            )
            last_dag_run = last_dag_run.filter(DagRun.dag_id.in_(filter_dag_ids))
            last_dag_run = last_dag_run.subquery('last_dag_run')
            
            
            last_task_instance_query_result = (
                session.query(TaskInstance.dag_id.label('dag_id'), TaskInstance.state.label('state'))
                .join(TaskInstance.dag_run)
                .join(
                    last_dag_run,
                    and_(
                        last_dag_run.c.dag_id == TaskInstance.dag_id,
                        last_dag_run.c.execution_date == DagRun.execution_date,
                    ),
                )
            )
            final_task_instance_query_result = union_all(