Apple installer will not accept my password

To authorize installation, you must provide a Mac Admin user login-name and its matching password. Your Apple-ID <anything> can not used for this purpose.

However, moments later, when the install completes and your new MacOS begins setup, it WILL demand the Apple-ID and password. For me, I always tell Apple-ID setup, "later, later" and just keep going with the rest of the setup. Then when the setup completes, I go back and provide the Apple-Id when everything else has settled. that makes any complications of Apple-ID setup easier to deal with "later".

I'm not sure I understand your question.

Your iCloud password and Mac login password are two different things. You'd use your login password to install apps on your Mac. Your iCloud password would be used to set up iCloud Mail and other iCloud services.

Am I missing something?