It is a huge pain to reinstall old macOS on old machines… on top of that, the tools to do a lot of this require Intel chipsets still. The official instructions say to just install the old installer from the App Store… but you can’t do that from an ARM machine. And the older installers will download, but they come as a DMG containing a PKG that runs a pre-check first… the pre-check fails because it is an ARM chipset.
Here’s what worked… I used the tool linked from this Reddit post at https://dosdude1.com/highsierra/… but I only used this tool to download the High Sierra installer… it has an option to create a flash drive, but I didn’t need that. Then I followed the instructions at https://support.apple.com/en-us/101578. I couldn’t actually get the High Sierra installer from the App Store because it requires an Intel machine, but the dosdude1 tool would download it anyway and bypass the pkg installer check. Once I got through that, I was able to plug it in to the iMac, hold option and then boot from it and start the install.