I have found an ugly workaround to finally remove artifacts but I doubt that things should work like this:

# simulate training process
for epoch in range(NUM_EPOCHS):

    # task.mark_started(force=True)

    artifact_name = f'artifact_epoch_{epoch}'

    # upload
    task.upload_artifact(
        name=artifact_name,
        artifact_object=PATH_TO_ARTIFACT,
        wait_on_upload=True
    )

    # remove
    task.delete_artifacts(artifact_names=[artifact_name])

    # remove for sure
    task = Task.get_task(task.id)
    task.delete_artifacts(artifact_names=[artifact_name], delete_from_storage=False)