The phone number (different from my number) in "trusted phone number" to sign in with two-factor authentication is WRONG

You need to change/add the number on your Apple ID. You may have to add the new number before you can remove the old number. After the change, allow up to 24 hours for the change to sync. Before trying to make the change, sign out of Messages/FaceTime on all devices/computers.

Apple ID - Manage 

My Apple ID is fine. My phone number in your records is no longer in use. New Number 415-***-****. NOT IN USE 646-***-****.

[Personal Information Edited by Moderator]

The code will not get automatically sent to the trusted number unless you specifically request it there.

See the steps in the support document you posted from under "Get a Text or Phone Call".

https://support.apple.com/en-us/HT204974

Get a text or phone call

If you don’t have a trusted device handy, you can have a verification code sent to your trusted phone number as a text message or phone call.

1. Click Didn't get a verification code on the sign in screen.
2. Choose to have the code sent to your trusted phone number.
3. You'll get a text message or phone call from Apple with your verification code.
4. Enter the code on your other device to complete sign in.

And, no, the number does not need to be added to the Apple ID to be a trusted number.

mrmuffet wrote:

My Apple ID is fine. My phone number in your records is no longer in use. New Number -. NOT IN USE -.

Please do not post your phone number in a public forum where anyone can get it. The forum moderators should remove it shortly for your safety. This is a user to user forum, and no one here can update your number. Only you can do that.

To update your Trusted phone number (which is different to the one associated with your Apple ID) for Two Factor Authentication, log into https://appleid.apple.com with your Apple ID and follow the steps here: link-> Two-factor authentication for Apple ID - Apple Support