Maybe as a common mistake, I read a number of "management" books before accepting the promotion. The one that stuck with me was Managing Humans by Michael Lopp. That is much more people skills and some planning.

Budgeting seems to differ significantly by company culture and practices, but is probably the easiest to get help with from peer managers or your accounting department.

Politics I have no idea.

I'm working on an app to help managers with the people / soft skills stuff. It helps with 1 on 1s, goals, and personal stuff for your reports.

Would love to talk to you if you're interested (check my profile for contact info).