As someone who dove deep into keychain items for a previous write-up, I believe you are misunderstanding this situation. As far as I understand it, many keychain items can be stored in your iCloud keychain. However, your local machine can have its own keychain that's different than the iCloud keychain, with items that are not sent to iCloud.

And besides all that, to my knowledge your local machine password (the password you use to login) isn't stored in a keychain item, so there's no way it could make itself into the iCloud keychain, or your local keychain.

You may be mistaking some explanations. Your computer password is used to unlock your local keychain, but it itself is not stored in your keychain. Your local keychain is also not your iCloud keychain, it's not stored in iCloud.

Again, I'm not an Apple developer, so there may be stuff I don't know, but I am a developer in general and I have researched this. The above is my current understanding.