Yes, same issue here. My original Venu (1) would update automatically whenever on charge, but the with Venu 3, I have to go into the music app and manually tell it to "update downloads".

This is happening me since last week too. A few nights no REM recorded at all, and I slept well last night. It worked after charging but is back to its old tricks today. 

But long pressing A should have triggered the restart or is it a shutdown?

If restart, then in my case it did not and the start happen once i plugged the charge/data cable. 

I would try manually installing a beta next time one becomes available. That may rejigger something internally. They are installed simply by copying the firmware file onto the internal storage using the charging cable.

So... No, issue isn't resolved. It seems to happen less frequently though: in particular, it looks like if I sync the watch after unplugging from charge, it doesn't drain as quickly (more testing required though)

Yes, the USB-A clip that comes with the Lily will also work on the Lily 2

USB-A Clip Charging/Data Cable | Garmin

You could also use a USB-C to USB-A adapter.

That's why I'm looking at an Apple Watch.  Updates go on for years.  And I don't care about charging daily.  When the new unit comes out and has BP and Sleep Apnea detection, I'm gone.