A new driver (v2.0.0) was released. Unfortunately, it doesn't solve the issue that I'm experiencing (no internet after wakeup from standby):
Direct link:
https://plugable.s3.amazonaws.com/bin/AX88179/ASIX_AX88179_DEXT_v2.0.0.zip
Source:
https://plugable.com/blogs/news/new-asix-driver-fixes-macos-11-big-sur-ethernet