@Brian: I received my invitation to interview about two days after the auto-reply; however, I’m very aware that my experience isn’t universal – I’ve seen posts by people who’ve waited several weeks between applying and hearing back (from a human). I can’t say what, if anything, that means: perhaps it varies depending on the role applied for, or the time of year, or perhaps recruitment is broken into “cycles”. Or maybe HR are just overwhelmed with applications at the moment as COVID makes more and more people discover that hey, remote working can work for them, maybe they should consider working somewhere that does it really well.

Sorry I don’t know more than that! Good luck!