Project management is a pretty saturated field, you are correct. Engineering team management is considerably less saturated and EMs are just as in-demand as ICs.
However, much of the value of a good EM is derived as someone who builds and grows a team over a long period of time, so you don't see nearly as much short-term job hopping as you do with ICs.
+1
Author here: the other thing is (at least for me) that it becomes really hard to leave my team after a while because they just grow on me. I feel responsible for their wellbeing and want to make sure they are set up for success. When I was an IC it was much easier (in my head).
Project management is a pretty saturated field, you are correct. Engineering team management is considerably less saturated and EMs are just as in-demand as ICs.
However, much of the value of a good EM is derived as someone who builds and grows a team over a long period of time, so you don't see nearly as much short-term job hopping as you do with ICs.