As far as I’m aware the only options to install GSR as a package are AUR/yay (not available on fedora as far as I understand) or flatpak (unable to resolve permission issue), so I do think a manual install is the best option. This is a gaming system so GSR breaking is no huge deal.
Thanks for the tips regarding manual installation! I did not know about -devel packages or about the dnf provides command. They will probably prove to be very useful!