Google's John Mueller had to confirm that you do not need to have a Google My Business verified business listing to show up in Google Web Search. You do need a Google My Business listing to show up well in Google Maps and in the local pack results or to show a local panel in search but not to rank in web search.
Someone asked on Twitter "Is (GMB) Google my business required to show your search results in Google?" John Mueller responded "No, it's not a requirement."
Here are the tweets:
No, it's not a requirement.
— 🍌 John 🍌 (@JohnMu) January 6, 2021
This is a screen shot of this site showing up in Google Search and there is no Google My Business listing for it. And yes, we get traffic from Google Search even without a Google My Business listing.
My business, RustyBrick, has both an organic listing on the left side and a local panel listing on the right side - that is the difference:
The two are really separate and are not dependent on each other. Although, if you are a business, it is highly recommended that you have a Google My Business listing so customers can find you in the local results.
Forum discussion at Twitter.