Here's an example I grabbed off the front page: post #5972082
The URL I got for this page when clicking the thumbnail is: https://danbooru.donmai.us/posts/5972082?q=ugoira+
There is no longer any download button or link. There is only "View WebM". This link goes to https://danbooru.donmai.us/posts/5972082?q=ugoira+ ...which is the same URL I'm already on. It doesn't take me to a .webm file. Right-clicking the image and choosing "Save image as..." will only download a single still frame. So it seems that downloading the whole animation is impossible now, at least without jumping through hoops that 99% of the site's users won't know how to do.