Sound in Linux virtual machines in Parallels Desktop 16 for Mac computers with Apple M1 chip is not supported.
If you have a USB headset, as a potential workaround for Parallels Desktop 16, you may connect the headset directly to the virtual machine if you prefer to stay on Parallels Desktop 16.5.
To do that, simply run the virtual machine and in the top menu click Devices > USB & Bluetooth and select the USB headset in the list.
With this approach, the sound is likely to work, but the quality may suffer. Meanwhile, when connected to the virtual machine, the USB headset will not be accessible on the macOS side.