When the peak swarm traffic hit, the Bounce rate jumped over 80% - typically this is in the low to mid 20% strata with usual traffic.
During the swarm surge I can confirm average engagement timed also dropped dramatically just like your analytics @piffy and there is also a corresponding drop this time as well.
I do not normally look at that metric but did because of you posted your graph. I think average engagement timed this or bounce rate are good flags that something is way off with the traffic quality and type.
Weirdly I am seeing another jump to almost 80% bounce rate on one days traffic but there is no surge. The traffic levels look normal i.e. pre-surge.
Analytics were delayed, there is a bit of a surge, about 30% of previous mega surge. Same pattern again. The only difference is CF is managing that pressure and the server is ticking along but this is not good as it is wrecking the user engagement metrics.