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
that's easily verifiable doing the searches yourself;
a search for "hvor ofte bør man dusje" in my english google, conencting from brazil shows havfruen4220.dk as 6th and 7th result, which is pretty high for a spam website
"hvordan regne prosent" shows 2 dk websites www.humanrebels.dk, and havfruen4220.dk as 9th and 10th results
could be since the OP clicked on these links to find out google made his personal algorithm show even more of this stuff
thus, I imagine a never ending cycle of even more spam could easily be generated, specially for an innocent user
It is Google that needs "incognito" mode, not the author.