How do I get over being intimidated by stakeholders and office politics?

You are good at the quiet part, the analysis, the thinking. Then the door opens and the room fills with people and their agendas, and something in you shrinks. That is not weakness. It is simply that you have practiced one skill far more than the other. The room feels big because you have not spent much time in it yet. Politics feels like a dark art from the outside. Up close it is mostly people protecting what matters to them and wanting to be understood. You already understand people through your work. You just have not trusted that the same care works face to face. It does. Pick one person, not the whole room, and have one real conversation before the big meeting. Ask what they care about and listen. Do that a few times and the intimidation starts to fade, because the room stops being a crowd and becomes a set of people you have actually talked to.