You have to actively select the subscription.
I got a new iPad and they have been sending me periodic notices about my three month tryout for Arcade. I did sign up for the three month News subscription but will cancel that.
I have Apple TV + which I pay for. I think I got three months free when I got the Apple TV device.
However, in your situation just do nothing because you are currently getting Apple TV+ for free. There is no reason for you to actively subscribe for a three month free trial since you already pay nothing for those three months.