Would I struggle much in a doctorate program?

You are an accomplished student. This won’t change. If this is what you want to do then go for it. Don’t worry about others. Worry about yourself. Will graduate school be more difficult. Probably and why it’s graduate school. Many people struggle to get through. But they finish and continue with their careers. Something tells me you will be fine. Yes, determination and persistence as stated always wins. It’s not really how smart you are. Many smart people drop out of graduate school or any school. Students with determination and persistence usually finish. How smart you are or your IQ is just part of the equation. It’s not the whole equation. Your gonna be fine. Good Luck.