A learning break could mean different things to different people, but it sounds possible the tutor is recommending an interruption in studies.
I like this wording, as it emphasises the temporary nature of the recommendation, if it is made. If this comes to pass it will be because experienced academics can see that your DD isn’t in the right place to succeed this term, yet they believe in her potential. They want her to get well and then rejoin her studies.
Generally this is the best plan and too many students make the mistake of persisting in the attempt to study whilst ill until they are in a very bad way, academically speaking. I commend the tutor.
Your DD is also correct that this is something she should manage for herself if she can. (Of course you should be available and supportive if she cannot). You generally have no legal access to information her university or its staff hold about her, though a true emergency is different.
Why are you wary about medication? There is a lot of evidence now that medicating the young can reset their brains and stop mental illness in its tracks. Are you concerned about side effects, or about the significance of having a DD on MH medication, which points up that she has a real MH problem? Because it sounds like she does, and she needs you.
The side effects are surely for DD to assess without prejudice.
I know it is difficult right now, but it is far from hopeless. DD can regain her health. This suggestion tells me her School wants the best for her. I have seen it work many times.
Best wishes to DD.