Hi there, I also experienced this issue (Catalina 10.15.2, Geany 1.36). I have replaced my Geany with [the version available here](https://download.geany.org/snapshots/geany-1.36_osx.dmg) (n.b. the file name is the same as my original install but the contents are different...).
Its early days yet but I have scrolled around in some files that were problematic and the issue seems to have disappeared.
I found this download via [the issue discussion here](https://github.com/geany/geany/issues/2344). That issue is on the face of it unrelated but fixing the screen painting seems to be a welcome side effect (maybe something to do with GTK changes on the Mac?).
Hope this helps!