I enjoyed an Elegant Puzzle but often felt it was targeted at a step above first time management, with topics on having interview pipelines, org design, etc. But it was still a good read.
His follow up book on Staff Engineering I think is a good read for first time managers. It lays out the other leadership path, which is helpful both for understanding where you fit in and the other leadership path you can guide your reports towards, based on their trajectory and interests.
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...