Hello and welcome. Thank you for telling us your story. I have to say upfront I have not been in your exact situation but I did walk away from my marriage.
Any relationship that is or was worthwhile is very difficult to leave. Having been in the depressed situation I know how I felt and frankly would have loved to have someone with me for support and comfort. Sadly I live alone so I had to battle mostly on my own although I had some support from friends and family. Do you have any family you can talk to? Friends? It is good to talk face to face. Writing on BB means delays between posts but we will be as quick as possible. Another alternative is contacting the 24/7 Beyond Blue helpline 1300 224636.
You are not responsible for your partner's mental health and when his problems start to effect your mental health I think it's time to take some positive steps to keep yourself well. I know when I left my husband I felt a bit guilty and perhaps you also feel a bit guilty. Please remember you are as worthwhile as your partner and in need of a safe place to live. Making plans is a good strategy even if you eventually decide not to leave. Once you have something in place I think it gives a feeling of comfort.
I understand your partner is reluctant to talk about anything but I wonder if you can get him to sit down with you while you explain what is happening for you. Things like his lack of engagement at home, refusal to stay with a therapist and give it chance to help and the effect of all this on you. You may also want to tell him you are thinking of leaving (but have your plan in place first). Knowing how I felt I'm not sure he will properly grasp what you are saying but it's important to make the attempt as he may start to realise the load you are carrying. It's also probable he does not have a lot of energy as this is one of the effects of depression and is often the reason people find it harder to stay with a therapist.
There are a couple of forums you may want to explore to get some tips. I know you are not a carer in the formal sense but this forum has lots of information. Supporting family and friends with a mental health condition (carers) It's worthwhile browsing. You could also take a look at Relationship and family issues
I hope this helps.