So I tried out Photo, Designer and Publisher in Bottles today (a Wine frontend) with the latest caffe-7.10-1 runner, and they all successfully installed and ran. I can open, edit, save and export documents like I can on Windows. Affinity Publisher can open large documents without crashing.
One big issue at the moment seems to be that the GUI is very glitchy and acts up when you hover over certain elements. Often entire windows can go black and only certain elements can show depending on what part of the window your mouse cursor is. Another issue is that clicking the "Edit in Photo/Designer/Publisher" option in the menu brings up an error message saying "Failed to launch designer - Could not hand over the file to the other application."
All in all, a big improvement over the last time I tried to get it running in Wine a couple of months ago, in which it wouldn't even run at all. We're not there just yet, but I have a feeling we're getting close.
Here are some screenshots: https://imgur.com/a/k3XpPuF