I looked at the Changelog for Core RP Library 14.0.6 and it appears I need to be in Unity 2022.2.4f1.
After updating my project to that Unity version, I am unable to get the package manager to understand that Core RP Library 14.0.6 exists. It does not appear in the Package Manager window, and trying to manually tell my manifest.json file to download it results in a "can't be found" error.