Sophie, I talk to young adults/children with mental health problems as part of my job.
You definitely are NOT responsible for your flatemate. The burden should not be on your shoulders. You are at university yourself to study and enjoy your life. From what you have said, you have been a good friend and done everything you can for your flat mate.
Sometimes when people are that depressed or have suicidal tendencies the only thing left is to seek medical advice and mental health advice. I see you have contacted student support and that your flat mate is on a waiting list to be seen by a psychiatrist. Sadly our mental health service is now beyond crisis and waiting times are unhappily the norm..often for many months.
In the meantime, your flat mate will not recover until expert help has been given. You have done all you can at this point. If your flat mate and their mental health issues are seriously impacting your quality of life, you must leave. You can calmly sit and tell your flat mate that while you support them and will always be a friend to them, the impact of their health issue is too much for you to bear, and so you must leave. Have this conversation calmly, but stick to your guns. Your flat mate may beg you to stay, threaten sucicide (and if they do call emergency services instantly) but your life and your university years are precious to you. Do not stay in this environment if it is impacting you severely.
Your flat mate will get help, but can only start to understand and recover from mental health issues IF THEY WANT TO. If your flat mate pushes help away, they cannot use you as a crutch to always be there for them. I know this is a form of tough love, but your studies and your own health must take priority here.
I hope this is of help,to you and I wish you all the very best, and your flatmates too.