At the moment the top of admin/config/search/settings contains options for reindexing content, and settings that apply to how content is stored in the index.
Of the default search pages, these apply to the content (node) search, but not to the user search. There is nothing in the user interface to explain that these settings apply only to the content search even indicate that the user search is not indexed.
Any solution needs to work with search pages provided by contrib modules. We do not know whether these search pages will be indexed or not.