If upgrading from macOS Sierra or later, your Mac needs 26GB of available storage to upgrade. If upgrading from an earlier release, your Mac needs up to 44GB of available storage.
macOS Monterey System Requirements
Apple has outlined specific hardware requirements necessary to run macOS Monterey. You can download and install macOS Monterey on the following Mac computers...
● MacBook Pro introduced in 2015 or later ● MacBook Air introduced in 2015 or later ● MacBook introduced in 2016 or later ● Mac mini introduced in 2014 or later ● iMac introduced in late 2015 or later ● iMac Pro ● Mac Studio ● Mac Pro introduced in 2013 or later
Apple recommends you install the latest Mac OS that is compatible with your device. If your Mac doesn't support the very latest operating system, you may still be able to upgrade to a more recent OS. Use software update or find links to download other macOS installers below...
Despite the message, it should have added the Install macOS Monterey app to your Applications folder. You can then run that app to complete your install.
After download,macOs Monterey 12.6.3 shows 11.7Gb but after completes it is 12.56gb and adds Install Mac OS X Ventura 13.2 (22D49) ? Monterey 12.6.2 works correctly shows 11.5GB when downloading then completes as 12.44gb.