I now seem to be on software version 3.80.
Trying to upload a new workout directly via Garmin Express and a USB cable was unsuccessful, but it did sync to the Garmin Connect app and from there to the watch. I've no idea whether the software update had anything to do with this. No other issues so far.
It's all gone very quiet here! I'm glad Garmin seems to have recovered from the recent massive outage.