Unpickled tensorflow model fails to make predictions

I've seen this question and this one, but neither actually explain what is going on, nor offer a solution to the problem I'm facing.

The code below is a snippet from what I'm trying to do in a larger context. Basically, I'm creating an object that contains a tensorflow.keras model, I'm saving it to a file with pickle using a trick adapted from this answer. See the code below ReproduceProblem.py:

import pickle
import numpy as np
import tempfile
import tensorflow as tf


def __getstate__(self):
    model_str = ""
    with tempfile.NamedTemporaryFile(suffix=".hdf5", delete=False) as fd:
        tf.keras.models.save_model(self, fd.name, overwrite=True)
        model_str = fd.read()
    d = {"model_str": model_str}
    return d


def __setstate__(self, state):
    with tempfile.NamedTemporaryFile(suffix=".hdf5", delete=False) as fd:
        fd.write(state["model_str"])
        fd.flush()
        model = tf.keras.models.load_model(fd.name)
    self.__dict__ = model.__dict__


class ContainsSequential:
    def __init__(self):
        self.model = tf.keras.models.Sequential()
        self.model.__getstate__ = lambda mdl=self.model: __getstate__(mdl)
        self.model.__setstate__ = __setstate__
        self.model.add(tf.keras.layers.Input(shape=(None, 3)))
        self.model.add(tf.keras.layers.LSTM(3, activation="relu", return_sequences=True))
        self.model.add(tf.keras.layers.Dense(3, activation="linear"))


# Now do the business:
tf.keras.backend.clear_session()
file_name = 'pickle_file.pckl'
instance = ContainsSequential()
instance.model.predict(np.random.rand(3, 1, 3))
with open(file_name, 'wb') as fid:
    pickle.dump(instance, fid)
with open(file_name, 'rb') as fid:
    restored_instance = pickle.load(fid)
restored_instance.model.predict(np.random.rand(3, 1, 3))
print('Done')

While is does not fail on the line instance.model.predict(np.random.rand(3, 1, 3)) it does fail on the line restored_instance.model.predict(np.random.rand(3, 1, 3)), the error message is:

  File "<path>\ReproduceProblem.py", line 52, in <module>
    restored_instance.model.predict(np.random.rand(3, 1, 3))
  File "<path>\Python\Python39\lib\site-packages\keras\engine\training.py", line 1693, in predict
    if self.distribute_strategy._should_use_with_coordinator:  # pylint: disable=protected-access
  File "<path>\Python\Python39\lib\site-packages\keras\engine\training.py", line 716, in distribute_strategy
    return self._distribution_strategy or tf.distribute.get_strategy()
AttributeError: 'Sequential' object has no attribute '_distribution_strategy'

I don't have the slightest idea of what _distribution_strategy should be, but in my workflow, once I've saved the file I don't need to train it anymore, just use it to make predictions or consult other attributes of the class. I've tried setting it to Noneand adding more attributes, but with no success.

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