### 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)

"""
        Returns edge information for the given pair of tasks if present, and
        an empty edge if there is no information.
        """
        
        empty = cast(EdgeInfoType, {})
        if self.edge_info:
            return self.edge_info.get(upstream_task_id, {}).get(downstream_task_id, empty)
        else:
            return empty
    def set_edge_info(self, upstream_task_id: str, downstream_task_id: str, info: EdgeInfoType):
        """
        Sets the given edge information on the DAG. Note that this will overwrite,
        rather than merge with, existing info.
        """
        self.edge_info.setdefault(upstream_task_id, {})[downstream_task_id] = info
    def validate_schedule_and_params(self):
        """
        Validates & raise exception if there are any Params in the DAG which neither have a default value nor
        have the null in schema['type'] list, but the DAG have a schedule_interval which is not None.
        """
        if not self.timetable.can_run:
            return
        for k, v in self.params.items():
            
            if not v.has_value and ("type" not in v.schema or "null" not in v.schema["type"]):
                raise AirflowException(
                    "DAG Schedule must be None, if there are any required params without default values"
                )
    def iter_invalid_owner_links(self) -> Iterator[tuple[str, str]]: