Exported Keras model missing 'train' tag-set

Hello, I created and compiled a Keras model in Python and saved it in the SavedModel format. I want to load this model in the TF C or C++ API for training and prediction.
Currently I’m able to do prediction with the C API, loading the ‘serve’ tag-set. However, when I want to load the model for training the ‘train’ tag-set is missing.
The output of saved_model_cli only shows the ‘serve’ tag-set.

TF Python: 2.5.0.
TF C API: 2.5.0-dev20210512

Model creation:

# imports from tensorflow.keras

# build model using the functional API
input = ...
output = ...
loss = ...

model = Model(inputs=[input], outputs=[output])
model.compile(loss=[loss], optimizer='adam', metrics=['accuracy'])

model.save("./model", save_format='tf')

Output from saved_model_cli:

$ saved_model_cli show --dir model
The given SavedModel contains the following tag-sets:

What am I missing?
Is this even possible?
Maybe this only works in TF 1.x?

Thanks in advance