Second the recommendations for "an elegant puzzle" and "the manager's path".

Cant believe this one has not been mentioned yet: "Becoming an effective software engineering manager" by James Stanier (https://pragprog.com/titles/jsengman/become-an-effective-sof...) - a good book, and very specific for exactly your situation.

Would also like to mention my own podcast "Ask an engineering manager" - more focused on SWEs, but also has some episodes about how to be an Eng Mgr, e.g. https://askanengineeringmanager.libsyn.com/017-typical-mista...