is any search engine infringing on copyright because it contains a snippet of the source page?
In some jurisdictions, it is. And in other jurisdictions, it is only allowed as long as it shows a link to the source page, which Copilot also doesn't do.
After all, if showing a search result in the IDE is “publishing” (let alone “selling” (?)) why hasn’t Google been sued out of existence for showing search results (oops, “publishing” copies of original work, billions of times over), as well as selling related advertising?
https://en.wikipedia.org/wiki/Fair_use
> Examples of fair use in United States copyright law include commentary, search engines, criticism, parody, news reporting, research, and scholarship.