I thought the Papal Encyclical was just opinion on church and spiritual matters - more or less. Acting as the Vicar of Christ, the statements would be made from St. Peter’s Throne and known as Ex Cathedra and, therefore, binding truth for all Catholics as doctrine.
Isn’t this so, Catholic brothers and sisters?
It is as you say.
It’s just a letter. Correct.
Though i am not a Catholic, and if i may post information without it being seen as being contentious flame baiting (which is disallowed), according to much church teaching I would have to say no, no, encyclicals and other papal public teaching, including social teaching, also normally requires assent.
Of course one must recognize not only the different levels of church teaching but the different levels of assent. If you want actual statements by popes and Catholics and can engage in civil exchange, then it would be best if you asked.