I'm considering to register a kubernetes cluster in Rancher. After that, how should I handle coming kubernetes upgrades? Can they be handled by Rancher itself?
I only found information about upgrading a k3s registered cluster.
You should be able to do it from the cluster view (if your cluster was installed via rancher) as documented:
From the Global view, find the cluster for which you want to upgrade Kubernetes. Select ⋮ > Edit.
Expand Cluster Options.
From the Kubernetes Version drop-down, choose the version of Kubernetes that you want to use for the cluster.
Click Save.