Mike, sorry to say, you're correct, Catalina 10.5.7 is the highest OS a 2012 iMac can install, and you'd loose more than gain likely..
macOS Catalina - Technical Specifications
General Requirements
- OS X 10.9 or later
- 4GB of memory
- 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
- Some features require an Apple ID; terms apply.
- Some features require a compatible internet service provider; fees may apply.
Mac Hardware Requirements
For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:
- MacBook (Early 2015 or newer)
- MacBook Air (Mid 2012 or newer)
- MacBook Pro (Mid 2012 or newer)
- Mac mini (Late 2012 or newer)
- iMac (Late 2012 or newer)
- iMac Pro (2017)
- Mac Pro (Late 2013 or newer)
How to download and install macOS - Apple Support
https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12
And caution on 10.15 or higher, to see which Apps will no longer work in 10.15 get Go64...
https://www.stclairsoft.com/Go64/
Only solution is a newer Mac to get GarageBand... unless you might fiind a used Mac with it installed.