Well, you actually only tried Lato and DejaVu fonts, monospace is an alias, usually of DejaVu. DejaVu is rubbish, I do wish distros wouldn't set it as default, but on my system here I can't see any difference between Geany 1.38 and 2.0 with DejaVu sans mono, and neither looks "blurry" until the point size is very small, and then they both show the _same_ AA effects, mostly on verticals.
It may depend on exactly the versions on your system of the font, of harfbuzz, of Pango, of Freetype, and the screen resolution, yes there are lots of moving parts, and each new Debian changes them (well not your screen, but the software ones).
I can't see anything wrong with your image of Lato, but maybe thats the screen capture and image rendering process.
Download and try [Hack](https://sourcefoundry.org/hack/)