In this story, I would argue that Krebs is presented to us as a static character and as a round character. He is definitely a character that does not change in terms of his core personality by the end of the story, even though he plans to change his actions to please his mother and those around him. He is, above all, a character who is characterised by his profound disconnect with society and with emotions. Note how he is defined in the middle of the story, when we are told that he is not interested in any romantic relationship:
He did not want any consequences. He did not want any consequences ever again. He wanted to live along without consequences.
Even though he promises his mother to get a job, he and we as readers recognise that the emotional atrophy that has occurred within him and that defines him to such an extent is something that is not going to fade away any time soon. He is a round character precisely because he is described to us in such detail and with such psychological realism, as the quote above testifies.