The LLM is first trained as an extreneley large Markov model predicting text scraped from the entire Internet. Ideally, a well trained such Markov model would use em dashes approximately as frequently as they appear in real texts.
But that model is not the LLM you actually interact with. The LLM you interact with is trained by somethig called Reinforcement Learning from Human Feedback, which involves people reading, rating and editing its responses, biasing the outputs and giving the model a "persona".
That persona is the actual LLM you interact with. Since em dash usage was rated highly by the people providing the feedback, the persona learned to use it much more frequently.