Call waiting notification

That is NOT how call waiting works. If you are on the phone and another call comes in to you you will be notified.

If you call someone who is on another call, you will hear it ring until it goes to voice mail or the other party answers.

Some carrier may offer the option to notify callers that you are on another call when a second call comes in, but that is up to the call recipient to set up with their carrier.

If the call receiver has disable "Call Waiting" (See Pic below) then you will not get the notification.

What you believe your carrier should do is between you and your carrier. The phone can't know that because the carrier doesn't tell it.

Contact your carrier.