Vlad I think they are valid examples? In every case there should be no results found, as the domains do not contain any pages with the other words in the query, and the other search results are all from other domains (which should be excluded by the site operator).
I selected those because it makes it very easy to see whether they are behaving as expected: any results are from other domains, and therefore the bug is present. For example, with a website as large as google.com, sometimes you need to go to the second page to see false results — and even if there’s nothing wrong there either, there’s no guarantee that it worked correctly, it could just be that none of the top 20 results were erroneous.
But sure, here are some more examples, with domains that have more content:
❌ site:google.com testing (as seen in the screenshot)
❌ site:google.com lorem ipsum
❌ site:kagifeedback.org test
✅ site:kagi.com test
❌ site:kagi.com test test
✅ site:kagi.com query
❌ site:kagi.com site
Also, I didn't give any actual examples of this earlier, so here's a sample filetype query with results that don't match the specified extension: oliver twist filetype:pdf
