[Remote State] Add mixed cluster tests for remote cluster state publication #16497
Description
Is your feature request related to a problem? Please describe
Right now there are no automated mixed cluster tests for remote cluster state. So if there are some breaking changes in new version, they will not be detected by the integ test suite.
Describe the solution you'd like
We need to have mixed cluster tests with remote cluster state publication enabled and test with all kinds of cluster metadata
Related component
Cluster Manager
Describe alternatives you've considered
No response
Additional context
No response