Why does bidirectional LSTM have half the parameter count compared to LSTM in keras?

I want to implement a unidirectional and a bidirectional LSTM in tensorflow keras wrapper with the same amount of units. As an example I implement the unidirectional LSTM with 256 units, and the bidirectional LSTM with 128 units (which as I understand gives me 128 for each direction, for a total of 256 units). The implementation details:

import tensorflow as tf
in_ = tf.keras.Input(shape=(28,28))

x = tf.keras.layers.LSTM(256)(in_)

model_unidirectional = tf.keras.Model(in_,x)
print(model_unidirectional.summary())

y = tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(128))(in_)

model_bidirectional = tf.keras.Model(in_,y)
print(model_bidirectional.summary())

However, looking at the models’ summary, the unidirectional LSTM has double the parameter count compared to the bidirectional LSTM, even if they have the same output shape in both cases:

model_unidirectional summary:

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_11 (InputLayer)        [(None, 28, 28)]          0         
_________________________________________________________________
lstm_11 (LSTM)               (None, 256)               291840    
=================================================================
Total params: 291,840
Trainable params: 291,840
Non-trainable params: 0
_________________________________________________________________

model_bidirectional summary:

_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
input_11 (InputLayer)        [(None, 28, 28)]          0         
_________________________________________________________________
bidirectional_7 (Bidirection (None, 256)               160768    
=================================================================
Total params: 160,768
Trainable params: 160,768
Non-trainable params: 0
_________________________________________________________________

Why does the bidirectional approach have significantly less parameters if their output shape is the same?

x = tf.keras.layers.LSTM(256)(in_)

y = tf.keras.layers.Bidirectional(tf.keras.layers.LSTM(128))(in_)