I've spent all of my career in various Project Engineer, Project Manager, and now the manager of the PM group in an office for a top 3 Global EPC company. I started in the construction side after college, and then moved to the engineering side of the business. Have run some small cap alliances, but the last period has been more Large Cap ($100-500M) size projects.
I have PMP direct reports, but I don't personally have that certification, but I do have my PE license, which is fairly unique for PMs at least in our company. The PMP is helpful for some of the "book" part of the PM world, but not much help in the real world of dealing with team members, clients, and subcontractors in my experience. I know when I'm interviewing PMs that if they start with "I am a PMP", they may not have much useful practical experience if they immediately start with the PMP discussion, kind of like interviewing engineers that start with, "I'm a PE".
In simplistic terms, I always tell people that want to become a PM, it's generally all about managing scope, schedule and budget. The usual tools, Excel, Project, P6, and any specific cost software (there are lots of them). Although for big projects you have a team of resources to help manage the cost and schedule, including using the tools, I haven't used Primavera personally since the P3 days. I can teach someone the tools pretty easily, the PM mindset is harder to teach, people either have it or they don't. We have lots of engineers who want to be PMs (as they strangely see it as the path to fame and fortune), but being a good engineer doesn't mean you'll be a great PM.
You'll spend most of your time problem solving. How to win a job, how to complete a job (on schedule/on budget) and how to get paid for a job. If you like problem solving, it can be a rewarding career path. But you have to like dealing with problems, ultimately that's what you get paid to do: problem team members, problem clients, problem subcontractors, technical problems, team in-fighting, corporate expectation problems, corporate lawyers, problem AHJs, etc.
In terms of career path, there are lifetime PMs. People that enjoy the hands-on Project Management role. Often they manage larger or larger projects, become project executives, or become the go-to "problem project fixer guy" of management. Some will have direct reports, but many of our senior PMs have no interest in managing people directly. Even in a company our size, the list of PMs that management will put on a $2B size project is pretty short. Certainly some move on to other positions, Sales, Ops Manager, or we lose some to our clients who hire them to manage companies like us.