How to write type hints when you change type of a variable?

Say that I have

def foo(x: Union[str, list[str]], y: Union[str, list[str]]) -> tuple[list[str], list[str]]:
     
    x = cast(Union[list[str], tuple[list[str], ...]], str2list(x))  
    y = cast(Union[list[str], tuple[list[str], ...]], str2list(y))  
    
    return x,y
     
def str2list(*args: Union[str, list[str]]) -> Union[list[str], tuple[list[str], ...]]:
    vals = []
    for x in args:
        if not isinstance(x, list):
            x = [x]
        vals.append(x)
    if len(args) == 1:
        return vals[0]
    else:
        return tuple(vals)
    

x = 'My name is x'
y = ['First element', 'Second element']

z = str2list(x,y)

As you see, there are two cast calls in foo, but still mypy complains that

error: Incompatible types in assignment (expression has type "Union[List[str], Tuple[List[str], ...]]", variable has type "Union[str, List[str]]")  [assignment]

A workaround could be to define new variables and adjust the return type of foo as it follows

def foo(
    x: Union[str, list[str]], y: Union[str, list[str]]
) -> tuple[
    Union[list[str], tuple[list[str], ...]],
    Union[list[str], tuple[list[str], ...]],
]:

    xl = cast(Union[list[str], tuple[list[str], ...]], str2list(x))
    yl = cast(Union[list[str], tuple[list[str], ...]], str2list(y))

    return xl, yl

But I would prefer to overwrite x and y rather than defining two new variables xl and yl.