Just a temporary solution, which is just a little bit better than copying hints each time, inspired by @InSync and the decorator in related question:

from typing import TypeVar, Callable
from typing_extensions import ParamSpec # for 3.7 <= python < 3.10, import from typing for versions later

T = TypeVar('T')
P = ParamSpec('P')
def take_annotation_from(this: Callable[P, T]) -> Callable[[Callable], Callable[P, T]]: 
    def decorator(real_function: Callable) -> Callable[P, T]:
        def new_function(*args: P.args, **kwargs: P.kwargs) -> T:
            return real_function(*args, **kwargs)
        new_function.__doc__ = this.__doc__
        return new_function
    return decorator

And use it as

from torch.nn import Module

class MyModule(Module): 
    def __init__(self, k: float):
        ...
    
    def forward(self, ...) -> ...: # with type hints
        """docstring"""
        ...

    @take_annotation_from(forward)
    def __call__(self, *args, **kwds):
        return Module.__call__(self, *args, **kwds)

And this solution may be proved if last three lines of the code above can be packed as something like macro, because it remains unchanged among different implementations of sub-nn.Modules.