How to completely delete an app from Apple Devices

re: "All the online help sites tell you to delete it on the iPhone then go to your Apple ID, enter the iCloud and delete it from there too. All the apps we have are listed on the Cloud. "

Apps cannot be stored in iCloud. App user data can be synced or backed up on iCloud, but not the apps themselves. If you delete an app and then want to download it again, it downloads from the App Store. The cloud icon in the App Store only indicates that it is an app that you have previously downloaded. I've no idea what online help sites your are referring to; there is no way to go to iCloud and delete an app from iCloud as apps are never and cannot be stored in iCloud.

re: "When I try to download the app again from the App Store I see the cloud symbol as you state but don't see a "get" symbol, so I click on the cloud symbol, it downloads the App and the old email address with it."

If you've downloaded the app before using the same Apple ID for the App Store, there won't be a "Get" option, only the cloud symbol (which does not have anything to do with iCloud).

I've never used two Apple IDs with the App Store but if you want to download an app you first need to be signed into the App Store with the Apple ID. Apps retain the Apple ID that they were originally dowloaded with and even if you delete the apps everywhere, it you go into the App Store while logged into the old Apple ID, it is going to do what you are experiencing. Creating a new Apple ID doesn't change the Apple ID that apps are associated with unless you use the procedure described in Change your Apple ID - Apple Support and it sounds like you didn't. You won't be able to do that now that you already have set up a new Apple ID.

It sounds like you are signed in with the old Apple ID when you go to the App Store to download that app. The following 3rd party article may help you sign in with a new Apple ID: https://osxdaily.com/2021/10/29/use-different-apple-id-app-store-purchases/

Apps cannot be stored in iCloud. If you delete an app and then want to download it again, it downloads from the App Store The cloud icon in the App Store only indicates that it is an app that you have previously downloaded.