Sounds like the document root (root directive inside of the Nginx configuration) is pointing to the wrong directory. I believe Forge lets you edit the Nginx config, so I'd suggest going into that site within Forge and ensuring the root file path is pointing to the document root of your site.
I'd guess this means Gitlab isn't installing correctly - as you say, the project directory disappearing would result in these errors. What you need to do is figure out why Gitlab Git isn't deploying as you suspect. Either the directory structure in your project isn't what you expect or Forge + Gitlab has issues communicating.