I think what you should do now is:
1 Because you were a collective account before graduation, and the head of the household is a school, and you are just one of them. Therefore, since the ID card is given by the school, you should go back to the school first. If you don't get the household registration certificate, ask them to reissue it for you.
I want to change my hukou back to Chifeng city, which is in line with the principle that the hukou will be moved from there to there. After your ID card is reissued, you can directly ask for the proof of account transfer in Chifeng.
Don't mention Chifeng ID card again. Talking too much makes it even more confusing.