As I can’t find a definitive and official method of doing this, the following is based on what appears to work best. With a little work in Terminal, it’s not hard to extend the capabilities of Recovery to include the installation of a different version of macOS. The latter have to be booted in Recovery with the USB stick attached in order to install macOS from the stick. Apple provides detailed instructions for creating that bootable installer in this article, which explicitly includes M1 Macs. You can combine the two and make yourself a bootable installer on a USB ‘stick’, which is the neatest solution. One way around this is to avoid using Recovery on the internal disk (or an external, for Intel Macs), start that Mac up from another disk and run an older macOS installer from there. This is an important consideration for anyone intending to install and test Monterey betas: even when you install a beta-release of macOS to an external disk, it will automatically update your Mac’s Recovery, and the version of macOS available in that will be that Monterey beta, not your previous version of macOS. Boot in Recovery and the only version which the standard tools will install is Big Sur 11.4. During the course of that upgrade, the installer will update the Mac’s firmware and its Recovery system to that for Big Sur 11.4.

Let’s say you were running Catalina, and upgrade it to Big Sur 11.4.

Within that, the Install macOS app which performs the installation can only install that one version of macOS. This problem arises because when you install a more recent version of macOS on any Mac, the macOS installer also updates its firmware, including the Recovery system. This article suggests ways to work around that, and install the macOS of your choice. If you’ve ever tried this, you’ll surely have discovered its big snag: in Recovery you can only install one version of macOS, and that’s the latest which has been installed on that Mac, which may be the one that you don’t want. For instance, if you just installed a macOS update or upgrade which is causing problems you can’t resolve any other way. Although you might want to do that because the system has become damaged, it could be because you want to downgrade macOS. When you boot your Mac in Recovery Mode, one of its key features is installing macOS.

Big sur installer