When I open Template: fedora-37 > Software, I can see applications and search, but when I click install, nothing happens. Do I need to enable network connection in the Template settings?
Templates don’t have network access by design, see How to install software | Qubes OS. You shouldn’t enable network access for a template, but rather use sudo dnf install <PACKAGE_NAME> for installing software in the template.
The Software app in the template is GNOME’s, not anything specific to Qubes. I haven’t had to use it myself, but it most likely tries to make network connections that aren’t using the updates proxy. It’ll still work in standalone qubes.