Apple One starts out with a 1 month free trial for all the component services that you haven’t tried before. For previous Apple TV+ subscribers, than means that Apple TV+ is not included in the first month.
For a seamless transition, users should account for one month overlap. The superfluous subscription will then be canceled automatically, at the end of the trial period. Else wait out the first month.
* The Apple One free trial includes only services that you are not currently using through a free trial or a subscription. [1]