Hugo has instructions for hosting on Netlify with a bunch of options you can set. If memory serves, this was easy enough to do with the default settings that it just works. I’m not using many of the Hugo features, nor any of the special Netlify features, so perhaps there will be an opportunity to revisit this.
The particular instance running now is pinned to an old version of Hugo. That will certainly cause problems in some future as Hugo changes from version to version. (Trying 0.79.1 instead of 0.69.2 to see what breaks.)