I have the exact same problem–the Gnome calendar doesn’t sync with my Evolution caldav calendar. For what it’s worth this works perfectly with opensuse tumbleweed on Gnome 3.38
I know this is an old thread, but the issue is still unresolved with Evolution when installed from Flatpak. I think the problem may be related to this report: Caldav in Gnome · Issue #11 · fedora-silverblue/issue-tracker · GitHub.
Similarly, Gnome Contacts fails to pick-up CardDav details from Evolution.
However, after trying different versions of Gnome Calendar and Evolution from Fedora and Flathub, I have found a solution. If you use CalDav, you need to install Evolution from the official
rpm. Now integrations work as expected.
I was experiencing the same issue as the OP. Installing the rpm package of Evolution instead of the Flatpak is what fixed it for me. Thanks for the suggestion!