How to update software from OS X Yosemite?

With two-factor, to log in on a Mac running Yosemite, see the following from Two-factor authentication for Apple ID - Apple Support

If you use two-factor authentication with devices running older OS versions—like an Apple TV (2nd or 3rd generation)—you might be asked to add your six-digit verification code to the end of your password when signing in. Get your verification code from a trusted device running iOS 9 and later or OS X El Capitan and later, or have it sent to your trusted phone number. Then type your password followed by the six-digit verification code directly into the password field.

Then see: How to upgrade to macOS Catalina - Apple Support

There is no way to turn off two-factor if it has been on longer than two weeks. See: Manage your photo and video storage - Apple Support

Two-factor does work in Yosemite and other older systems if you follow the directions posted in my previous reply. You enter the password followed by the two-factor code, both together where you would normally only enter the password.