I was very saddened to read your post. At a time when you probably need each other more than ever, it must be heartbreaking that your husband has effectively shut you out.
Equally the raw mix of emotion you are experiencing must make things even harder changing as I suspect they do, often more than once per day.
A few things come to mind, observations really rather than anything practical but which may perhaps help you make some sense of the situation and hopefully help you cope a bit better.
First, he may not be deliberately avoiding talking about his Parkinson’s. As he is not currently receiving any treatment, support or seeking help, it may be easy for him to
pretend, maybe deny, it is happening therefore 'what’s to talk about
This is probably going to sound ridiculous but there may be something in that three years on from diagnosis he is managing without treatment or support; he might think it would be tempting fate if he started to talk about it. Not as far fetched as it might appear - a friend of mine won’t watch live England matches because on too many occasions when he has they have lost and when he doesn’t they win!
If your husband is not naturally a talker when it comes to emotions, this would be unlikely to be different because it’s Parkinson’s.
I’m guessing here of course but hopefully therr is something in there that resonates with you.
As for what you can do, I see you have already some replies which I hope helped. I have been trying to think what I might do in your shoes and my blue sky thinking resulted in this:
It’s important that you look after yourself. Whatever the eventual outcome it will mean little if your health breaks.
Play the long game smartly. By that I mean don’t make a big deal out of his lack of communication. Keep it low key and drip feed when the opportunity arises - perhaps he mentioned a small thing in passing, maybe you have read something, maybe make a comment which requires him to say more than yes or no but is positive - perhaps an opening gambit could be along the lines of "do you realise it’s been 3 years since your diagnosis and I don’t know what I thought was going to happen but it certainly wasn’t that you’re still holding your own without any treatment or support
Just because your husband is 'going it alone doesn’t mean you have to. You can of course use the forum as you have done today and the helpdesk but, with the lockdown hopefully coming to an end you may wish to consider joining a local support group and meet people living with Parkinson’s and their carers. What you choose to tell your husband is up to you but his Parkinson’s does affect you too and he needs to understand that if he won’t discuss it, you need some support from somewhere.
Following on from this last point it may perhaps be worth considering writing him a letter setting out what you think and how you are feeling. You will have given him a way in without what he may see as a threatening conversation, and he can choose how to respond. It will need to be carefully written but could perhaps give you a way forward.
I don’t know if any of this will be feasible or possible as obviously I don’t know either of you nor anything of your relationship, but hopefully there is something in there somewhere that helps.
Take care and wishing you well.