Thanks for the proper details, I have checked the configuration and found the problem.
By default the plugin only looks for published items and nothing else, so I suspected some kind of misconfiguration.
What I have found that on the General Options -> Sources 2 panel you had every taxonomy selected to return as results, which I'm not sure you wanted at all. So the problem most likely was that some taxonomy terms (like tags, categories) were also in the result list, at some of them might had the same names as posts or products.
I simply turned all of them off, tried a few search phrases against unpublished items, but I don't see any in the results, only published ones, so it should be all right now.Best,
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