What has been the most surprising thing about being a Director that you only realized after you were promoted?
Many promotions happen because the person was already performing and showing up as being at the next level. Depending on the company, the Director role marks a clearer line between individual contributor roles and management roles. However, unless the promotion is accompanied by a significant change in scope or new formal reporting lines into the role, perhaps the most surprising thing is that much else remains the same. You might now be on some additional distribution lists for Directors and above, but most of that is also related to people-management.
Leveling up to Dr level meant being a point of contact for many people at the company, which meant more inquiries from sales, customers, leadership, and other product teams. Since I got promoted, my inbox and # of slack messages doubled :)
My learning from this experience is that you want to document as much of the process as possible so people outside of your team can find SMEs and relevant information for your area.