Downloading again should work on the installed computer. Here is an explanation:
"The installer is deleted by the system after the installation is complete. If you go to the Mac App Store and press the Option key while clicking "Purchases," you should then be able to download the installer again. (If the installer file already exists on your system then the App Store will not let you download it again.)


On a Mac since 1984.
Currently: 24" M1 iMac, M2 Pro Mac mini with 27" BenQ monitor, M2 Macbook Air, MacOS 14.x; iPhones, iPods (yes, still) and iPads.