### Apache Airflow version

2.2.3rc1 (release candidate)

### What happened

I ran a DAG that does nothing explicitly with context, so I'm surprised to see deprecation warnings about context being used (trimmed to cut down on noise):

```
baseoperator.py:1107 DeprecationWarning: Accessing 'execution_date' from the template is deprecated and will be removed in a future version. Please use 'data_interval_start' or 'logical_date' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_ds' from the template is deprecated and will be removed in a future version. Please use '{{ data_interval_end | ds }}' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_ds_nodash' from the template is deprecated and will be removed in a future version. Please use '{{ data_interval_end | ds_nodash }}' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'next_execution_date' from the template is deprecated and will be removed in a future version. Please use 'data_interval_end' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_ds_nodash' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_execution_date' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'prev_execution_date_success' from the template is deprecated and will be removed in a future version. Please use 'prev_data_interval_start_success' instead.
baseoperator.py:1107 DeprecationWarning: Accessing 'tomorrow_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'tomorrow_ds_nodash' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'yesterday_ds' from the template is deprecated and will be removed in a future version.
baseoperator.py:1107 DeprecationWarning: Accessing 'yesterday_ds_nodash' from the template is deprecated and will be removed in a future version.
```

### What you expected to happen

I'd only expect to see deprecation warnings about things my DAG is actually interacting with.

### How to reproduce

Run this DAG:

```python
from datetime import datetime

from airflow import DAG
from airflow.operators.bash import BashOperator

with DAG(
    dag_id="no-context", schedule_interval=None, start_date=datetime(2021, 12, 10)
) as dag:
    BashOperator(task_id="sleep", bash_command="echo 'Hello!'")
```

Note: I also tried a TaskFlow DAG and that wasn't impacted.

### Operating System

MacOS 11.6

### Versions of Apache Airflow Providers

_No response_

### Deployment

Virtualenv installation

### Deployment details

_No response_

### Anything else

This was introduced in #19886 (cc @uranusjr).

### 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)

tests/conftest.py
if "run_id" not in kwargs and "run_type" not in kwargs:
                kwargs["run_id"] = "test"
            if "run_type" not in kwargs:
                kwargs["run_type"] = DagRunType.from_run_id(kwargs["run_id"])
            if "execution_date" not in kwargs:
                if kwargs["run_type"] == DagRunType.MANUAL:
                    kwargs["execution_date"] = self.start_date
                else:
                    kwargs["execution_date"] = dag.next_dagrun_info(None).logical_date
            if "data_interval" not in kwargs:
                logical_date = timezone.coerce_datetime(kwargs["execution_date"])
                if kwargs["run_type"] == DagRunType.MANUAL:
                    data_interval = dag.timetable.infer_manual_data_interval(run_after=logical_date)
                else:
                    data_interval = dag.infer_automated_data_interval(logical_date)
                kwargs["data_interval"] = data_interval
            self.dag_run = dag.create_dagrun(**kwargs)
            for ti in self.dag_run.task_instances:
                ti.refresh_from_task(dag.get_task(ti.task_id))
            return self.dag_run
        def create_dagrun_after(self, dagrun, **kwargs):
            next_info = self.dag.next_dagrun_info(self.dag.get_run_data_interval(dagrun))
            if next_info is None:
                raise ValueError(f"cannot create run after {dagrun}")
            return self.create_dagrun(
                execution_date=next_info.logical_date,
                data_interval=next_info.data_interval,
                **kwargs,
            )
        def __call__(