vault-search is run by one person for their own use. With read-only Google Drive access, it copies that person's Drive files to their own home server and builds a search index there. Pages and text are sent to a computer on the same private network to compute the index; nothing is sent to any other party, sold, or used for advertising.
Only the owner can sign in. Removing the app at Google account connections ends Drive access; the copy and index are deleted with the service.