The proper way to play Byzantium in EU4 is to follow a literal day by day guide of what to build, destroy, and who improve relations with diplomatically. People will reroll starts until you get the right nations to have right opinion of you before you launch a war based on cheesing the way the AI "thinks," and they're far from the hardest start in game.
You weren't talking about not having other things to do, you were complaining that starting as difficult nations followed the same basic playbook. If we want to talk about what there is to do in the game, that's fine, but please pick a complaint and stick to it because it's impossible to talk about this if you keep changing your criticism.