What finally worked for me was installing the macOS 12 beta from inside the recovery mode: Download the Monterey installer app onto your internal SSD. Boot your M1 Mac into recovery mode by shutting it down first and pressing + holding the Touch ID key. Connect your external drive and format it using Disk Utility; choose APFS as file system. Disk Utility can also be used to unlock your Mac's internal SSD in case it's File Vault 2 encrypted. Still within the recovery mode, open Terminal, navigate to the Monterey installer location (probably ~/Downloads on your internal disk) Start the installation process by executing ./Install macOS 12 Beta.app/Contents/MacOS/InstallAssistant Note that the installation may take significantly longer, especially towards the end.

This solution ceased to work with the latest beta. Does anyone know an alternative? I really don't want to display my Big Sur app icons in previous macOS versions. Changing the DockTile is suboptimal as it only works after the app has launched, of course.

@vslavik: While this works, wouldn't it mean that the Mac App Store still shows the old icon, though?

@Luca1719 I'm afraid that doesn't work. Xcode (12.0 beta 4) always displays the svg with black paths as soon as I drag it into an .xcassets.