All info is using the Audioengine D3. Unknown if these issues apply to other DACs as well. These issues likely apply to any DAC/amp setup, based on ArchWiki.
The problem was originally noted when using the D3 (via a USB extension cord but same issues occurred when plugged directly into motherboard) on an ASUS ROG Strix B350-F Gaming motherboard. When playing any audio over the DAC, it was severely distorted with a constant metallic bit-crushed effect. This issue was resolved when plugging the DAC into a USB2 port on the motherboard rather than a USB3 port.
After switching motherboards to an MSI B550-A Pro, the issue returned, even when using a USB2 port. After troubleshooting again, I found that the problematic lines were these two config lines in /etc/pulse/daemon.conf:
default-fragments = 2
default-fragment-size-msec = 2
Changing the default-fragment-size-msec parameter to 5 resolved the distortion issue. ArchWiki (as always) has a relevant section with the same findings, suggesting that these issues are caused by a too-small fragment size: https://wiki.archlinux.org/title/PulseAudio/Troubleshooting#Setting_the_default_fragment_number_and_buffer_size_in_PulseAudio
However, I am unsure why for the B350 motherboard, connecting to a USB2 port allowed me to use a 2ms fragment size, while connecting to a USB3 port didn't.