I noted that a similar question from a few years ago (Shinyproxy-demo in Fedora 29 doesn't work) but without any discussion so I’ll add this.
I have installed docker and installed shiny proxy (2.5.0) from the rpm that is available from shinyproxy.io on Fedora 34. I have enabled these services and modified the docker service with the override.conf file in system.d as described in the getting started section of the documentation. However, as was previously mentioned in the post I mention above, when I visit the webpage localhost:8080 I get no response.