When I click a field to open a search popup, the columns in the search table are usually too narrow.
I always have to manually change the width of the columns
I’m using the Tryton 5.0 Debian buster packages.
My monitor is a 4K monitor with HiDPI.
The font size is really good on this monitor, it is easy to read. The only problem is the column width. I will try it on a non-HiDPI monitor later to compare this problem with column widths.
The width of the columns are fixed and indeed the value do not take into account the resolution of the screen. The font size is the one defined by your desktop environment or the GTK default (or the value you’ve set in the GTK config but people usually don’t do that), so we’re not responsible for this good choice 
We’ve recently discussed the issue of the behaviour of the client wrt the different resolutions of the screen found in the wild and finally found another solution. We could use some kind of scaling factor (some terminal do that) but I am not sure it would be useful given that the size of the columns you’ve set should be restored the next time you open your tree view (although I wonder what it will look like if you switch from your “normal” laptop to your 4K desktop and then back ; I am not sure it will be the behaviour we’re expecting).
Use latest version most of the views are much better.