Outside of engineering, a lot of people with "manager" titles are similarly engaged. Their supervisory work, while important, is about 4 hours of work per week. The rest of the time is spent on tasks assigned to them, such as creating a new process for replenishing the hand sanitizer, or approving documents.
It's just that we believe that by now we should have eliminated clerks, so to make ourselves seem modern, we re-title them engineers and managers.
I'm not saying that's a bad development. It's just what it is, probably follows a smooth bell curve distribution of expertiese. The hard stuff is just, like, really hard (as is English!)
This makes total sense to me. The bulk of time I’ve spent on many projects goes into supply chain management and factory coordination. I can easily see how the work of one engineer can keep 10 people like this busy full time.
In my work, the title "manufacturing engineer" title goes to people that work all day (and at a hard pace) doing nothing other than working in the PLM system, orchestrating ECO bureaucracy, and BOM work. To them, the actual products are nothing more than a collection of part numbers and rules applied in a cumbersome framework. I almost feel sorry for them. The sad thing is, there's an increasing population of these types, along with product/project managers and supply-chain specialists, while at the same time a decrease in engineers and techs.
I also have a physics educational background and make my living doing a weird mix of EE, software, and failure analysis work. I love my job, I see myself as a kind of general purpose problem-solver. Unfortunately actual hands-on technical generalists, IMHO, are in a downward spiral these days as far as status within large organizations goes.
The OP, I hope, is aware of this. He might be happier specializing in his interests and teaming up with other specialists who focus on EE.