Do most people end up in project/program management? I haven't been out of college that long, but I keep getting interviews and offers for jobs that have less and less engineering involved.
I suspect that it's related to the phenomenon of engineers running out and getting an MBA for the heck of it. In grad school for management, easily 75% of my classmates were engineers. Meanwhile my grad school's engineering school has dwindling enrollment. This is because in many organizations the path to the top (and the salary associated with it) is through the management career path, without as many opportunities (or any) for high level technical leadership.
I did manage a program for about 18 months and it was just NOT my cup of tea. Dealing with a useless supply chain manager, suppliers who didn't want to respond to me for literally weeks/months on end, getting hit with one technical failure after another, and handling a micromanaging boss who blamed me personally for those technical failures. Sounds like a real thrill, eh? I was thankful when we were able to kill the program and I could go back to being a technical lead. Being technical lead is great - I'm fortunate to be in a position to choose my own (small) pet projects, to work on a variety of interesting tasks, and NOT be sitting in the spotlight when senior management reviews the program. Being PM meant doing stuff that I could do, I just didn't LIKE it.
Fortunately my organization has preserved something of a technical leadership path that does not involve management. There are some really smart engineers who outright chose not to take a management path and I respect them for that. I think that for me, despite my master's in management, I do not want to go off the technical path, and I'm lucky that they won't try to make me.
I hope you're able to find an organization and position that allows you to stay in engineering if you choose.