### 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)

"""
    Class to hold the default value of a Param and rule set to do the validations. Without the rule set
    it always validates and returns the default value.
    :param default: The value this Param object holds
    :param description: Optional help text for the Param
    :param schema: The validation schema of the Param, if not given then all kwargs except
        default & description will form the schema
    """
    __version__: ClassVar[int] = 1
    CLASS_IDENTIFIER = "__class"
    def __init__(self, default: Any = NOTSET, description: str | None = None, **kwargs):
        if default is not NOTSET:
            self._warn_if_not_json(default)
        self.value = default
        self.description = description
        self.schema = kwargs.pop("schema") if "schema" in kwargs else kwargs
    def __copy__(self) -> Param:
        return Param(self.value, self.description, schema=self.schema)
    @staticmethod
    def _warn_if_not_json(value):