Menu links broken, but only when deployed

When I view the source of your site, I see that the href attribute has no value.

It would be helpful if you provided a link to the public repository for your project.

See https://discourse.gohugo.io/t/requesting-help/9132.

Let us see your code

Include a link to the source code repository of your project, because we really need the context of seeing your templates and partials to be able to help you. It is trivial to do a quick git clone on your repo, then run hugo server in your project, to help you out. On the other hand, recreating your code from screenshots, or sort of guessing at it, is not.

If you can’t share your repository for whatever reason, consider creating a dummy repo that you can share, which reproduces the problem you’re experiencing.