Right. This is an aspect I'd forgotten about. When I first arrived, the developers thought is was really weird for me to not only sit in, but have some pretty strong opinions about the subjects under discussion. They got used to it pretty quickly, but my upper managers didn't know what to think about it.
Huh? If people are having a technical discussion or architecture decision.. it seems totally reasonable for an EM to want to be involved and aware of what is going on. That's not weird. The best managers I've ever had are aware of technical details at a high level decision POV
You're told in no uncertain terms that it's not what you're paid for. You can do it "for fun", but it won't help on your evals even if your contribution to the discussion was critical (well, hopefully it still helps if thanks to that your project doesn't derail), and will be negative to you if you prioritized it over other "manegerial" taks.
That's one reason we sometimes saw managers just leave for a startup where nobody gives a shit about titles.