Welcome here, it was very sensible to find out how others have coped, your problem is sadly not uncommon.
Actually you have two problems, your own welfare and that of your partner.
Let's talk about you first. For anyone trying to deal with a partner who may be suicidal it is a frightening thing, and the pressure to 'fix' things, or at least give support, can be overwhelming. Add to that your existing conditions of anxiety and depression and you end up placing more strain on yourself that many could bear.
We tend to regard ourselves as being stronger, more capable and more resilient than is the case when it comes to supporting a loved one.
So may I suggest that you talk with your GP or therapist and set out what is happening, getting medical help and supervision to keep you as well as possible and avoid the pitfalls of falling ill yourself?
Can I ask if you have anyone to support you, family or friends perhaps? Trying to cope in isolation is very hard indeed.
The other thing, which applies to your partner too, is that there is professional help if feeling lost or overwhelmed. The Suicide Call Back Service (1300 659 467) is one very good example and specifically helps with those in your situation as well as your partner's.
Now your partner. The first thing to realize is that nobody keeps someone else alive all by themselves. It is a team effort, the people around, the medical team, the person themselves. The responsibility is shared.
This of course means your partner needs to seek medical help himself. Without his cooperation things can deteriorate, he needs to realize help is available and things can get so much better. I'm an example. I was suicidal, now I'm glad I'm here.
He too may wish to call a crisis line.
One activity you can both take part in that may help ease your mind a little is for you to assist your partner in making a Safety Plan. It is filled up with all sorts of things that can help, not just contacts, but whatever has brought pleasure or happiness in the past -or even simple calm. I've YouTube clips as part of mine.
There is a good free one here:
When one driven to want to take one's life it can be something easy to reach for instead.
You did say you were unsure what to do. Apart from above I do remember that my partner's presence, and the knowledge she would always be there was a comfort (even if I did not show it properly at the time)