Apple TV Plus does come for free for those on a student Apple Music plan, which is separate from the 12 month offer. That is what you were accessing, and since you have now been moved to a standard plan you no longer have access to that.
In order to claim the offer you would have to setup your new device (iPhone) and subscribe to Apple TV Plus on that device, which then comes with 12 months free instead of the standard trial. You can then access the service on other devices, but the initial claim needs to be done on the qualifying device. The offer is also only valid for 3 months from purchase date. As per the terms you cannot combine it with another trial or offer so you may no longer qualify and/or have exceeded the time period.