Shirou could have a range of reactions. He might be excited if the future in the fanfic seems positive and full of achievements. He could be worried if it shows him facing great difficulties or making bad decisions. And he might be amused at some of the more outlandish ideas in the fanfic.
Another possibility is that Shirou might go along with it for a while to understand Illya's motives better. He could be thinking that there is a deeper reason behind her actions and by staying with her in this situation, he can figure out what it is and then find a way to resolve the situation without causing more harm or trouble.
Perhaps they face challenges from the magical world. Since Saber has a connection to the throne of heroes, there could be threats from other entities who don't want a married Saber. They would have to fight together to protect their relationship and their new life. Meanwhile, they are also growing closer and deeper in love as they face these difficulties side by side.
Yes, the Beastars manga has come to an end. It left fans with a memorable and impactful conclusion that tied up the various storylines and character developments.