Interesting. This happens because of the caching done by the search component, which lasts for 15 minutes. I agree with the sentiment though - archiving a page is to get it out of the way, so having it show up in search is rather detrimental. Also worth noting that only cached pages can be searched in this way, the backend does not return archived pages.
I've assigned this one to Alli for now, however this will probably require a compromise between teams. Reducing the caching duration could be an option, but that will come with extra load to fetch recent items more often (longer loading times for the dialog itself). Another option could be to attach archived status to pages once they come back from the backend, but that requires and additional loading state + the potential for jank.
This bug was today raised by our users. I am hoping to see a fix vey soon.