There was an 1920*1920 monitor (https://www.inputmag.com/reviews/square-monitor-eizo-flexsca...) but that's over 1k USD :(
There are other nice displays like Huawei's Mateview at 3000*2000 but nothing costs less than ~550-600$/€. It's a bit of a pity because you can get a decent 1080p or even 1440p monitor for much less.
Fyi I had written a comment some time back on how to make your own monitor, using Panelook but that also isn't very cheap (edit here - https://news.ycombinator.com/item?id=30422163)