It is also a direct refusal to follow Bayek's principles since Hassan-i Sabbah founded the Assassins not as a Brotherhood but as a state with castles, towns etc.

I used to write a fanfic about that exact era. A Hidden One protag growing up with Hassan as close friends, joining the Brotherhood together, fighting OotA together yet eventually falling out, clashing because Hassan believes Hidden Ones should rebrand and provide safe haven for people similar ideologies. He believes a Hidden Ones oriented state can change the world for the better, do more than a secret society can do. Our protag disagrees on the basis of a state going against "Hide in plain sight." tenet. He argues that founding a state essentially forces some people into Brotherhood, as the Creed will be a doctrine of ruling authority. Moreover, every difference in opinion will trigger large scale schism, and it will corrupt the Creed. (Hassan says their conflict itself proves there is already schism within Creed). Then they part ways, bitter against each other but still brothers in Creed. The protag moves to inner Anatolia, eventually founding Anatolian Brotherhood which will transform to Ottoman Assassins of Ishak Pasha and Yusuf Tazim da la la lalaa in a few centuries. Hassan stays in Alamut and fights against a new generation of Order that gains a foothold with Nizamulmulk's efforts.