I do not think accessing other user's search history (Elastic Search Results) is feasible, as it will be privacy concerns.
However in HCM, if your query related to transactions by direct reports, that could be tracked.
Ref: What is the impact to HCM History When User ID (OPRID) Is Changed for an Employee? (Doc ID 2151783.1)
This depends on the type of search you are asking for, a search in the Navigator or global search uses Elasticsearch. Search strings used against Elasticsearch indexes will be logged in the msglog.html of the integration Broker.