New iPhone transfer did not bring AirTag info from old phone

I just got a new iPhone SE 3rd generation to replace my iPhone SE 2nd generation. I just when through the automated migration process of transferring over all info while holding the phones close. Seemed to have worked well. But I was surprised to find that the *Items* tab of the *Find My* app knows none of my AirTags. 👉 Is there a way to bring over those AirTag registrations? Or must I re-register AirTags with the new phone from scratch? If re-registering is required, is the proper route that is described in Apple Support page, *How to reset your AirTag* , where you remove, replace, and press the battery inside the AirTag five times?