Display virtual adapters in network settings
Finally, I found the answer in the Parallels knowledge base (https://kb.parallels.com/125286):

Issue
After upgrading macOS to Big Sur, Connect Mac to this network
and Show in System Preferences options disappeared from Parallels
Desktop preferences &gt; Network..
Show in System Preferences option can not be selected so Host-Only
network cannot be found from macOS System Preferences &gt; Network.
Cause
These features are now hidden due to macOS Big Sur restrictions
(KEXT-less network mode): In macOS Big Sur Apple restricted usage of
kernel extensions and Parallels Desktop does not load them by default,
instead it uses macOS own built-in mechanism.
Workaround
Downgrade to Parallels Desktop 16.0.1 or earlier - make
sure the version is compatible with macOS Big Sur.