Are you saying that there is a path for a partitioned index to have stats today? If so, we can just follow that locking protocol. If not, I'm concerned about trying to define the locking protocol for doing so as a side-effect of this work.
A quick test on v17 indicates that, no, there is no path for a partitioned index to have stats of its own, so I'm fine with removing RELKIND_PARTITIONED_INDEX from the allowable relkinds. The partitions of the partitioned index have stats but the umbrella index does not.
Wouldn't it be easy enough to issue a WARNING and skip it?
