Twinkly effects (movies) are not stored at device, but every time you select one are uploaded from phone. So you are asking for impossible. What can be done with 2022.12 is to have one effect loaded to device from phone and being activated/disactivated from HA integration.
While technicly it might be possible to intercept upload process to Twinkly, each movie is customized to specific lights configuration on the tree during mapping process, so even uploading this from HA and playing on specific Twinkly setup would most likely cause garbage effect…