Why KernelCare extension shows the error:
PLESK_ERROR: unsupported kernel,
contact helpdesk.cloudlinux.com for more info
Plesk installed inside of the container
It is an expected behavior. According to the list of supported OSes, KernelCare service should be installed on the Virtuozzo hardware node where containers are hosted, due to the fact that all containers use single kernel and there is no need to apply patches inside of the containers:
Note: That Virtuozzo ReadyKernel can be installed on Virtuozzo hardware node as alternative solution to install kernel patches.