How do I stop needing to feel like I belong at work?

You have found a quiet kind of freedom: you no longer need to feel certain that you belong. You just do the work, and the old fraud feeling has lost its power over you. Notice how you got here. You did not finally collect enough proof. You simply stopped making the feeling the boss of your actions. That is the real cure, and it is worth understanding so you keep it. Belonging was never something you had to feel before you could act. You act, you contribute, and the belonging is demonstrated in the doing, not granted in advance by a comfortable feeling. You gave up waiting for a permission that was never coming. The fraud feeling may still knock now and then. Let it. You have learned you can do good work without answering it, and that is the whole skill. When it shows up, treat it like weather: noted, not obeyed. You are past needing its approval, and that is exactly where you want to stay.