No one knows but I am not as pessimistic as I was 6 months ago. My guess is applications don't increase significantly, and that with the vaccine rolling out, financial markets doing well, and universities not being as financially hurt as they thought, most programs are going to accept a normal class.
I think the biggest issue is going to be the number of deferrals from last year. I'm not sure the extent of this either, but it seems like there were a fair number of 1st year PhD students who decided to defer entrance from Fall 2020 to Fall 2021. This might limit the number of incoming spots -- interested if any current students/faculty members can comment.
Also: a number of programs have messages on their site that they'll be taking fewer students than normal this year. My assumption is it will be a tougher year, but not orders of magnitude more competitive.