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.
Topic:
App & System Services
SubTopic:
Core OS
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