The problem resolved itself this time before any update on Avast's end.
But as you requested for details, I manually updated the Avast application version when I saw in the Update tab that the version was in red, indicating that it needed updating. So I clicked Check for Updates, it did its thing, I rebooted, and then for the next two to three days Windows Spotlight didn't show the tips and whatnot. As I stated before, this has happened before, and it always coincided with an Avast update, for whatever reason. But Spotlight now works again, so I'm happy.