Hi, full marks for this post. All the info present and easy to read. Thanks!
aplay -l shows you have two soundcards present: the onboard one and your HiFiBerry DAC+ Pro. Since you mention it working in your web browser you must be using the Desktop version of Raspbian rather than the Lite version. I don’t use it, but if I remember correctly they configure which soundcard to use in the file /home/pi/.asoundrc. This allows programs running as user pi to use the correct soundcard. However, Mopidy as a service runs as user mopidy so it’s not privy to that information.
Assuming I am right and there is something to that effect in /home/pi/.asoundrc you can copy it to /etc/asound.conf so that programs running as other users (i.e. Mopidy) can use the correct settings.
Alternatively and maybe simpler is to just disable the onboard soundcard entirely so there is no chance of confusion. I believe this is still the recommended approach as documented in the HiFiBerry install guide.