This gets complicated!
First Apple has moved on with newer versions of the apps so you might encounter an issue trying to get them from the Apple online App Store (not iCloud). So first try logging into the Apps Store using the Apps app on your system. Are you able to down load them from there at all? Or do you get a warning you need a newer macOS.
Even still you should be able to get the older version of the apps for your macOS you are using. Most people have a backup of their stuff to restore to their system do you still have it? That would be the easiest way, restoring it to your new system. If that’s not possible, see if you can find a friend with a Mac that is using an older version of the apps having them make a backup of their apps using Time Machine so you can restore them onto your system (apps only not the user accounts) even if they are older you should be able to upgrade to a more workable version for your macOS version from the App Store.
You might find an independent servicer locally who has copies of the older versions to help his customers. I would give that a try, they may ask for a fee for the service.
The last way is buying a copy of the older versions from an online seller (the very last option)
There is no requirement to use iCloud here in any way. Apple runs all of their apps On System and mostly free, they have never required active connections to their servers to run any of their apps. Now with that said, you might have a shared library of elements in a work place on a server (yours) or for safety use iCloud to store your created files so if your system where to fail you have a backup or want to share them directly.
What you are thinking of is Microsoft’s approach with Office 365 which offers an Online free version or paid subscription version, or a On System version at a higher cost.