I’m afraid the limit for owls on one page in Hugo is 3, though there is an issue in the tracker about making it a config parameter.
That was a joke, I don’t know what that has to do with the issue you are having. 
Your content is in your theme. That is unusual. If you need to edit anything in your theme, override the theme templates in your site’s layouts directory.
For instance, you added the second client section to /themes/airspace-hugo/layouts/partials/work.html, but the site uses layouts/partials/work.html for that page, per the template lookup order.
If I were you, I’d move the stuff out of the theme into your site’s layouts, content and static.