### 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_type = inferred_run_type
            elif run_type == DagRunType.MANUAL and inferred_run_type != DagRunType.MANUAL:
                
                raise ValueError(
                    f"A {run_type.value} DAG run cannot use ID {run_id!r} since it "
                    f"is reserved for {inferred_run_type.value} runs"
                )
        elif run_type and logical_date is not None:  
            run_id = self.timetable.generate_run_id(
                run_type=run_type, logical_date=logical_date, data_interval=data_interval
            )
        else:
            raise AirflowException(
                "Creating DagRun needs either `run_id` or both `run_type` and `execution_date`"
            )
        if run_id and "/" in run_id:
            warnings.warn(
                "Using forward slash ('/') in a DAG run ID is deprecated. Note that this character "
                "also makes the run impossible to retrieve via Airflow's REST API.",
                RemovedInAirflow3Warning,
                stacklevel=3,
            )
        
        copied_params = copy.deepcopy(self.params)
        copied_params.update(conf or {})
        copied_params.validate()
        run = DagRun(
            dag_id=self.dag_id,
            run_id=run_id,