Mojave will not upgrade to Catalina using Installer

Instead of using that link, try to use this link: https://support.apple.com/en-us/HT211683

Scroll down and select the Catalina link to download the installer. Your Mac can upgrade to the latest macOS 12 Monterey if you wanted it to, but if you want an older version, use that link (I have personally used it before and it worked for me).

1) Backup your Mac with Time Machine: https://support.apple.com/en-us/HT201250

2) Erase all content and settings on your Mac through Disk Utility: https://support.apple.com/en-us/HT208496

3) Go through the setup process of a new Mac, but don't put any of your files or apps on it. Set up a "disposable" Mac account that you will remove later.

4) Try to download the Catalina installer from this empty Mac and follow the instructions to install it.

5) After the installation process of macOS Catalina, you will want to wipe the "disposable" Mac account. Repeat only Step 2

6) Now set up your Mac with your preferences and your new Mac account. When prompted to transfer info from an older Mac, use your Time Machine backup to transfer your files and apps (NOTE: macOS Catalina and higher doesn't support 32x bit apps)

7) Complete the setup process with your files and apps on macOS Catalina.

Is one using Safari to attempt the download as Others may not work ?

It is working from you link in above message on this computer as per picture below.

I just can not download it because this computer is TOO New and does not Qualify to run Catalina