Hi Christo. I'm 99% sure that it was the powered hub that solved your issue.
Here's my reasoning:
1. You had no issues playing local files. This proves that your DAC hat and rune installation are both fine.
2. The DAC draws power from your pi not an external power supply. This meant that you had a WiFi adapter, DAC and thumb stick all powered from the pi. Combined they require more current than the pi can provide. This also explains why lowing the volume in alsamixer improved the problem, lower volumes require less current. The same applies for the original WiFi adapter, it probably requires less current to operate.
3. Experience, I have a creative sound blaster x-fi USB DAC that I cannot use with my WiFi adapter without a hub. If I try to play music from Spotify or a network share I experienced similar problems as you, possibly worse as my runeui session would disconnect and it was hit or miss whether it would reconnect when I refreshed.
If you have a spare SD card, flash runeaudio and try streaming Spotify with the original components connected via the hub and no other changes.
Edit: corrected a few words.