Should we do literature search in Incognito mode?
It's probably good to resist treating any search engine as a "black box." That is, you probably should not simply accept the results without suspicion. 

There are a number of factors that affect Google searches. Your search history, if you are doing the usual thing, is clearly one of them. Just a few pages explaining this.

https://www.bluecorona.com/blog/google-ranking-factors-2018

https://www.wsoaonline.com/does-your-internet-history-effect-google-search-results/

https://www.webpresencesolutions.net/7-reasons-google-search-results-vary-dramatically/

https://www.link-assistant.com/news/personalized-search.html

What it means is, private browsing would not hurt. And you probably should not stop with Google. You should probably use a bunch of search engines. Bing, Yahoo, DuckDuckGo, the archive searches on any journal archive you can get that is relevant, more if you can.

And you should be aware of the possibility that somebody has paid to have certain search results pushed up the list. Possibly on more than one search engine.

And then you should carefully examine the results to see if what you have achieved has validity. You should try to unravel any bias or detect any gaps as far as reasonable. Look at your data the way a hostile competitor would look at it and try to detect any flaws before you send it to a journal.

For example: Is there a point of view you are aware of that has been left out? Even if you think that POV is totally wrong, having the search engines decide for you could be embarrassing. Is one point of view clearly given undue precedence? Even if you prefer that POV you should be concerned if a search engine offered you only stuff you agree with. Is one source artificially cloned into multiple sources? Is a group of sources, that you know to be independent, artificially collapsed into a single source? And so on.