This is what my mac has in the system info: iMac (21.5-inch, Mid 2011). All of the upgrade links in that link you provided point to the apple store that is not listing any upgrade for me. That's the problem. Everything points to the apple store and the apple store is not listing these upgrades.
So this (below) doesn't work because it points to the apple store and does not find the software to download.
Use the App Store
To download macOS from the App Store, use a Mac that is compatible with that macOS. If your Mac isn't compatible, the App Store dims the Get button, says that the macOS is not compatible with this device, or says that the requested version of macOS is not available.
If these links don't work as expected, try again using Safari, which is in your Applications folder.
Sonoma 14
Ventura 13
Monterey 12
Big Sur 11
Catalina 10.15
Mojave 10.14
High Sierra 10.13
- Use these links to find macOS in the App Store.
- Cick the Get button in the App Store to begin downloading. Software Update might open and ask you to download from there.
- After downloading to your Applications folder, the installer opens automatically. Follow the onscreen installation instructions. Or quit without installing to leave the installer in your Applications folder for later use.