For engineers who become managers, manager tools is my first recommendation as well. It can be cringy from time to time, but it really focuses on things we are not used to think much as engineers. And it gives a lot of practical tips one can use right away. I think they apply to almost any type of organisation large enough to require management.

One issue with giving tips about eng. management is a bit like giving tips about software engineering: it is very context dependent. Especially around the areas where you have agency. Do you have agency in hiring ? In the directions your team work on ? On head count ? On technologies ? On firing ? On promotions ? Depending on your levers, your management will have to adapt a lot.