Skirting the official macOS system requirements to run new versions of the software on old, unsupported Macs has a rich history. Tools like XPostFacto and LeopardAssist could help old PowerPC Macs run newer versions of Mac OS X, a tradition kept alive in the modern era by dosdude1’s patchers for Sierra, High Sierra, Mojave, and Catalina.
For Big Sur and Monterey, the OpenCore Legacy Patcher (OCLP for short) is the best way to get new macOS versions running on old Macs. It’s an offshoot of the OpenCore Hackintosh bootloader, and it’s updated fairly frequently with new features and fixes and compatibility for newer macOS versions. The OCLP developers have admitted that macOS Ventura support will be tough, but they’ve made progress in some crucial areas that should keep some older Macs kicking for a little bit longer.
I always love the dedication of these people trying to get macOS to run on hardware it was never intended to run on. It must be a small scene, actively fighting Apple every step along the way, but usually succeeding in the end. These are people giving older Macs a longer lease on life, and that’s only to be applauded.