Does anyone know a place to download install high sierra.app directly? Apple makes it impossible now.

I have a 2020 27" iMac running Catalina 10.15.7. I have a 2007 21" that needed a new internal HD, which I replaced with a good wiped and re-formatted HD. (tests fine). What I cannot do is get that machine to download or in any way get Sierra installed on it. I am trying to build a USB install disk for it. What happens when I try to download an install for Sierra from apple instructions found at https://apps.apple.com/us/app/macos-catalina/id1466841314?mt=12, it leads me to the App store. Pressing "GET" prompts my computer Update window which starts a fruitless and endless search for Sierra. It gets worse. I did manage to find and download InstallSierra.dmg and InstallSierra.app. The DMG file is useless since it gives up InstallSierra.pkg which is not usable for making USB install disk. ???. On my Catalina machine, no possible combination of the Terminal commands will create the installer. The thumbdrives will not eject. I spell them correctly, terminal tries to obey but just stalls out, eventually shutting down. I don't understand what I'm missing in what should be a very simple and straightforward act: install an older mac system on an older mac with a new hard drive.

Any help would be delightfully appreciated. - Jay

Thanks, I was confused dealing with three different macs on the counter here. The target machine with the new HD to upgrade is a mid-2011 21" , 12,1 with a top system of 10.13.1 (High Sierra). I am trying to make my own installHighSierra USB. Apple no longer lists Sierra as a possible older OS, so you say I need to go back and install el capitain and then upgrade that? (https://support.apple.com/en-us/HT201372)

Using the Catalina machine, I can't make the USB installer because it will not eject for reformatting with the Terminal command.

sudo /Applications/Install\ macOS\ High\ Sierra.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume

and I am parsing it correctly with the name of my USB. It will not eject and the process hangs. Any suggestions? Do I have to use a mac with High Sierra or El Capitan to do this?

Tell me you have successfully done this using these instrutions and made an install USB from the result.