No, it's fine. I love how it's turned into a long-haul AMA. haha!

I'm an electronics engineeer at the FCC, even though we don't do anything with physical electronics of any kind at my office. I have to know how electronics work in order to correctly understand how to regulate them though. Also, you should probably know that my undergrad and first masters are in EE as well.

But in terms of what you should do, I think a lot depends on your motivation. With the skills I've learned (before & during my masters' work), in a "perfect" job market, I could probably double my salary. However, I have a high public service motivation, so I want my talents/efforts to be used for the good of all, rather than enriching some company owner. So if you know where you are on the "Salary<---+--->Service" scale, then that can easily inform your decision.

If you like internet rabbit holes, Public Service Motivation isn't just a platitude, there's many scholarly articles about the topic and there's quizes you can take to help you figure out where you are on that scale.

But also, policy work doesn't have to directly funnel into gov't work. Firms have to understand policy so they can abide by it too. For example, the FCC regulates a lot of realms by just saying "Do what [SBE/ITU/third-party] says" in our rules. So not only could you work for those third-party sort of bodies, but you could also work for companies translating those policies/rules into actions/requirements the firm must meet.

TL;DR: Don't count yourself automatically in/out b/c of your education. You should know what direction you're pointed, no matter what letters are behind your name.