As an engineer or analyst, most of your world revolves around being given a problem to solve for.
This has its benefits of having helped you develop the technical skills of designing a solution, using the tools and methods and implementing the changes to provide your expected results. When you're given a clear problem, technical skills will ensure that you are building the thing right. But when you're discovering and validating which problems to solve, you must ensure that you're building the right thing.
Shifting to a post-technical lens means focusing on discovering problems and leaving the problem solving to your team.
In most cases, you're going to have a designer who has the technical skills that can help you research, interview and mock up your prototype. You'll most likely have an analyst that can help you query and analyze your data that you need to understand and capture. Engineers and architects are the people that will have the technical expertise to design the best solution given the requirements and constraints.
Your arsenal of technical skills have been decentralized to your cross-functional team to help you accomplish your objective.
This brings an importance of knowing how to sythesize your data into making decisions. An important soft skills that's going to progress your product along very well. You're going to have to convince not only your stakeholders, but your team that the endeavor you're about to ask them to invest in will yield value for the user as well as your business. You must be able to communicate clearly and concise updates on your roadmap, changes to your specification and release information.
Technical skills have gotten you to speak the same language and have a shared understanding, but you're going to need to adopt the soft skills to build rapport, trust and relationships with your team, stakeholders and users. As technology continues to change, it is a continuous learning process to keep up with the status quo. But as humans, the way we engage tends to change much less over time. To be able to sell, influence, prioritize, make decisions and communicate in all mediums is going to take you much further in your ability to lead in your post-technical career.