Gradient of MSE with Respect to w and b

Implement:

def mse_gradient(
    input: np.ndarray,
    weight: np.ndarray,
    bias: np.ndarray | None,
    target: np.ndarray,
) -> tuple[np.ndarray, np.ndarray | None]:
    """
    input:  shape (batch_size, in_features)
    weight: shape (out_features, in_features)
    bias:   shape (out_features,), or None
    target: shape (batch_size, out_features)

    Returns:
        grad_weight: same shape as weight
        grad_bias: same shape as bias, or None if bias is None
    """

Use the same forward pass as 01-hypothesis-function's linear, mean-reduced over every element the way 02-mse-loss reduces.

Do not use an autograd library. These are the manual derivatives.