InvalidArgumentError: cannot compute MatMul as input #0(zero-based) was expected to be a float tensor but is a double tensor [Op:MatMul]

Part 1: The problem is indeed the datatype of your input. By default your keras model expects float32 but you are passing a float64. You can either change the dtype of the model or change the input to float32.

To change your model:

def make_model():
    net = tf.keras.Sequential()
    net.add(tf.keras.layers.Dense(4, activation='relu', dtype="float32"))
    net.add(tf.keras.layers.Dense(4, activation='relu'))
    net.add(tf.keras.layers.Dense(1))
    return net

To change your input:
y = y.astype('float32')

Part 2: You need to call the function that computes your model (i.e. model(data)) under tf.GradientTape(). For example, you can replace your compute_loss method with the following:

def compute_loss(model, x, y):
    pred = model(x)
    return tf.reduce_mean(tf.square(tf.subtract(pred, y)))