Why does Apple ask for my confidential Mac password?

On my Mac (macOS Ventura), a daily notification asks me to update my account settings because some iCloud data could not be synchronized. When I get to System Settings, this message pops up ("The password you use to unlock this Mac will also be used to access saved passwords and other sensitive data you store in iCloud.").

Similarly, this message pops up when I try to login to my Apple account ("Continue to sign in on Safari for the user. Enter your password to allow this"). When I enter my Apple ID password, it is rejected.

I suspect I am supposed to enter my Mac's password here (FileVault). But this is a fundamental no go. I will NEVER EVER send that password anywhere online, whether it's Apple or any other organization.

Why does Apple need to know this extremely confidential information which is supposed to be exclusively in a user's head and never leave the confines of the local hardware?