### Apache Airflow version

2.5.1

### What happened

Context: I am attempting to use [TypedDict](https://docs.python.org/3/library/typing.html#typing.TypedDict) objects to maintain the keys used in DAG params in a single place, and check for key names across multiple DAGs that use the params.
This raises an error with `mypy` as `params` expects an `Optional[Dict]`. Due to the invariance of `Dict`, this does not accept `TypedDict` objects.

What happened: I passed a `TypedDict` to the `params` arg of `DAG` and got a TypeError.

### What you think should happen instead

`TypedDict` objects should be accepted by `DAG`, which should accept `Optional[Mapping[str, Any]]`. 

Unless I'm mistaken, `params` are converted to a `ParamsDict` class and therefore the appropriate type hint is a generic `Mapping` type.

### How to reproduce

Steps to reproduce

```Python
from typing import TypedDict

from airflow import DAG
from airflow.models import Param

class ParamsTypedDict(TypedDict):
    str_param: Param

params: ParamsTypedDict = {
    "str_param": Param("", type="str")
}

with DAG(
    dag_id="mypy-error-dag",
    # The line below raises a mypy error
    # Argument "params" to "DAG" has incompatible type "ParamsTypedDict"; expected "Optional[Dict[Any, Any]]"  [arg-type]
    params=params,  
) as dag:
    pass
```

### Operating System

Amazon Linux

### Versions of Apache Airflow Providers

_No response_

### Deployment

Docker-Compose

### 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)

"""
    Run a single task instance, and push result to Xcom for downstream tasks. Bypasses a lot of
    extra steps used in `task.run` to keep our local running as fast as possible
    This function is only meant for the `dag.test` function as a helper function.
    Args:
        ti: TaskInstance to run
    """
    log.info("*****************************************************")
    if ti.map_index > 0:
        log.info("Running task %s index %d", ti.task_id, ti.map_index)
    else:
        log.info("Running task %s", ti.task_id)
    try:
        ti._run_raw_task(session=session)
        session.flush()
        log.info("%s ran successfully!", ti.task_id)
    except AirflowSkipException:
        log.info("Task Skipped, continuing")
    log.info("*****************************************************")
def _get_or_create_dagrun(
    dag: DAG,
    conf: dict[Any, Any] | None,
    start_date: datetime,
    execution_date: datetime,
    run_id: str,
    session: Session,
) -> DagRun:
    """