I solved the issue - it was a bad install. We have installed older version of ES 7.9.2 directly from ES repo. This now matches my dev environment.
Apparently sysadmin installed previous ES from some random repo (CentOS/RHEL Packages Repository - GetPageSpeed) and not directly from ES repo.
So that might have been one of the issues.
We also removed Java and reinstalled it.
Once that was done, ES is singing now. No crazy GC every 5 seconds. All issues went away.
The only thing I changed on the new install was heap size 31GB and name of the node / cluster. Everything else left as is.
Thanks for the help @warkolm!