Edit: I guess I'm not surprised to see the downvotes on this; I get that a lot of people on HN don't really understand product management, or don't value it. The path from engineering to product management can really start with getting closer to the customer - putting more time into understanding their needs.
The reason this shifts a lot with LLMs is that a sales engineer / forward deployed engineer can tackle customer needs much more quickly with Claude Code than they could have themselves, which means these feedback loops can become a crash course in customer experimentation and understanding.
Teresa Torres wrote an amazing book about continuous discovery that I use with my teams (https://www.producttalk.org/continuous-discovery-habits/), and a third of the book is about talking to your customers every week if you can. Someone in a customer facing role who can also build code has a huge leg up compared to someone coming at product from an academic setting. Case studies in an MBA are great for strategy, but they're usually fixed points in time. Getting that nimble feedback to hone your product sense is the hardest part of getting good.