Is there a way to see the top searches that have been performed over a period of time?
Topic on Extension talk:CirrusSearch
CirrusSearch doesn't have any similar functionality. It does have low-level logging which could be batch processed to aggregate the top searches, but from CirrusSearch's perspective it logs the request and never thinks about it again.
I guess this is a feature request that could be added as a task to Phabricator?
In my opinion it wouldn't really be a feature request for CirrusSearch. This seems more like asking for an analytics platform to be built into MediaWiki, which CirrusSearch could then piggy-back off of to provide analytics over search requests such as top queries.