Okay, I published the test post and my links are not working on my published page either.
Just an FYI for others reading this. Once I sort this out I will be deleting the test page so if you arrive here in the future expect the link to my test page to be dead.
I am thinking that my issue might be how I am posting. I am not using goorgeous. I had read that org-mode was a first class citizen like markdown so I assumed that it should just work. Also, it appeared to just be working. I can write my content in org-mode and, render the page locally, and browse it. The only issue that I ran into so far is linking with anchors.
You mentioned previously that goorgeous is unmaintained now. It does look like the last commit was in November of last year. If goorgeous is required for proper org-mode support and it is not maintained then gohugo needs to state that org-mode support is not being maintained as a first class citizen.
Thank kaushalmodi for all of your help.