Can't download Catalina from App store or install package from Apple website

You've downloaded an updater, not an upgrader. See How to upgrade to macOS Catalina.

Open Safari, do not use Firefox and click on the link,

How to Upgrade to macOS Catalina again.

When you go to Section 4 click on Get macOS Catalina

this will redirect you to the App Store Catalina download page,

it should say Get or Download.

If it says Open then the App Store is detecting a copy of Install macOS Catalina.app

in your Applications folder, move it to the Trash, empty the Trash.

Connect your mac to your router via cable, Restart your mac

try again. Do not use the mac while it is downloading or any

other devices that share the same internet connection.

The download is large at 8.24GBs and you should really have

at least 30GBs of free space to accommodate the installation.

The update you downloaded from the Apple Support Downloads site is just an update

and requires you to be running an earlier version of Catalina before you can apply it.

Moving from one OS to a newer OS is called an upgrade and can only be done

using the full install package downloaded via the App Store.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates.