I'm really sorry to hear about what you're going through at the moment. I've recently just went through something similar to you as well (minus the 'live with me in the same house' part), and it is a really awkward and painful situation to be in...
On one hand, you want to support them as friends. But on the other hand, you're going through a lot of hurt because of the sudden break up without any prior warning. In the initial weeks after the break up, it may seem like they're fine, and messaging them almost seems like nothing has changed. This could give you a lot of confusion, and unsure how to approach her while trying to keep yourself together. As Geoff said, they may be different from day to day. It's very hard for us to tell whether she's okay or not with the lack of emotional connection from her. Glad to hear she's taken the initiative to see a doctor for a mental health care plan, that's a positive sign.
Being the person receiving the break up, it's hard for us to accept what has happened. I can only imagine it must've been more hurtful to you since you were both in a relationship together for 4 years... What felt like everything was fine and happy, only to be severed all the sudden. You're really strong to still be keeping in contact with her, while enduring the pain from the break up. I did that too to my ex during our first month of the break up, and it wasn't easy at all... Anyways, if I could provide you some additional advise along with Geoff's and Smallwolf's, take care of yourself as much as you can. Give yourself as much self-love, and fill your time with activities that makes you happy. Trust that your friend will be able to make it through this dark times of hers. It's okay to be checking in and reminding her that you're here for her if she ever needs someone to talk to. Don't be afraid to communicate your boundaries to her too.
Your friend is going through a battle that she does not wish for you, the person whom she once loved, to be apart of. She's afraid that if she drags you into her battle, she might hurt you. A person going through depression has a heavy sense of guilt, and she would be feeling guilty for having to put you through this heart break pain, except she still has a lot of things from her depression to get through first before processing that guilt (thus the emotional numbness when someone's overwhelmed by depression).
Wishing the best for the both of you. Take care, and happy to chat more if you'd like.