Is eks 1.28 is compatible with jenkins 2.387?
AFAIK, EKS itself should not care. We run 2.440 LTS on top of EKS 1.29 and it works just fine, although it does need a pile of hard learned tricks in order to scale.
I strongly recommend that you do not run 2.387 since it contains several known vulnerabilities and in general you want to always run the latest LTS, if only to ensure proper security.