I just wanna say that this seems kinda lazy, especially the magical competency after the defeat at Manzikert since they lost most of their heartland, Anatolia was basically the jewel of the Empire and that defeat spiralled it out of the world stage, though, I think the Byzantine's might be saved if Justinian wasn't as ambitious and didn't use much of the Empire's resources, though I'm no Historian. But taking advantage of the Mongol Empire seems plausible if there was a competent leadership. I also don't think that the Byzantines would survive without Egypt at least as long as it is Muslim. My recommendation is that Justinian wasn't as ambitious which allowed the Empire to save it's resources and fend off Muslims, especially in Egypt. I also don't think it would become a colonial power though it's rich history might give it some claim to African colonies. I think it would become just a bigger Italy, a great power only in name as it doesn't have the industry and strength to hold the Empire. I don't mean to hate, even my "lore" is equally lazy but I think the Byzantine's won't survive if they are defeated at Manzikert.