We today running rancher v2.6.3 with RKE clusters based v1.21.9, i would like to know if there is any compatibility issue with these versions before we go to production? Thanks!

https://www.suse.com/suse-rancher/support-matrix/all-supported-versions/rancher-v2-6-3/ Looks like v1.21.7 is the highest on the list under the 1.21 branch

should we upgrade rancher to 2.6.4 or 2.6.5?

I generally always upgrade to the latest stable version, we've been using 2.6.5 and it's treated us well. It also has 1.21.x as it's supported version https://www.suse.com/assets/EN-2.6.5SupportMatrix-300422-0116-26.pdf

is it possible to upgrade rancher from web ui? can you share a link how to update? thanks

I'm not sure there's a button to click, but should be possible to use the kubectl shell for it. https://rancher.com/docs/rancher/v2.6/en/installation/install-rancher-on-k8s/upgrades/

Thank you