I think there are two possible causes,
1. If this is the same tone you get when first connecting the charger, the charger may be disconnecting then reconnecting (at least logically if not physically), so it would be worth testing with a different USB power adapter and magnetic cable, according to what you have available. I know you have the adapter which charges your iPhone, so that would be perfect for testing.
2. Something actually wrong in the watch, either software or hardware. Software is a prime suspect because it started with the update. You could try unpairing and re-pair to your phone again to force reinstalling the Watch software. If that still doesn't work the last resort is Contact Apple Support and arrange to get it checked by Apple. Don't just skip to calling Apple Support, make sure you already tried the earlier steps because they will want to try these first.
Don't forget you can charge your watch at any time, you don't need to wait until overnight for testing the fixes!