I had to modify the code from Fedora Discussion so it works for Fedora Silverblue 36 users who upgraded from 35.
Before you run the command, confirm the version of the RPM Fusion repos you need to uninstall by running:
rpm-ostree status
Once I did that, I knew how to modify this code before running it in the terminal:
rpm-ostree update \
--uninstall rpmfusion-free-release-36-0.2.noarch \
--uninstall rpmfusion-nonfree-release-36-0.2.noarch \
--install rpmfusion-free-release \
--install rpmfusion-nonfree-release
After a reboot, this cleared up the issue with RPM Fusion repo updates in GNOME Software.