Very few of the skills overlap even within the same categories such as architecture and execution. One is about the code, the other one is about the people.
Once the core skills are developed e.g. being able to clearly communicate a vision and plan, ability to have tough conversations, building interpersonal trust, being an effective salesperson for the team. Once these skills are adequately developed, it becomes a good job again.
Most people have spent at least a few years training to become a professional software engineer before being able to do that job, and yet most engineers don't give themselves/others the same understanding for developing the necessary skills to become a professional engineering manager.