What do you expect incognito to change? That would presumably show the same content the author is seeing. Only Google sees the content that drives the ranking.
It is Google that needs "incognito" mode, not the author.
I stopped using google for search because I noticed the filter bubble it was building around me. Perhaps that wasn't maintained by cookies, but in that case I wonder what it was...
For all we know (as the OP doesn’t mention trying incognito) the OP could have malicious software on their device that hijacks their browser to manipulate search results
