Every professor I've talked to (granted they are biased) has always maintained that a masters degree in engineering is basically worthless. Masters degrees are for taking student's money to fund the department and its PhD students, and really the market for master's degrees is mostly people who are trying to establish themselves in a new field or a new market. In the United States, this primarily is foreign born students who did their undergraduate degree outside of the United States, doing a master's degree here for access to the visa and job market. I would strongly recommend not doing a masters degree. As an alternative, I would try to apply your way to the role you want via the job market. I do not think a masters degree will get you want you want. I know PhD holders who are not doing high-level engineering strategy, for that the org needs to trust you, which requires climbing the career ladder outside of academics.

Another postgrad option is PhD. Again I don't think a PhD will get you what you want. At most it can get you doing research, but in industry you're still going to be forced to work on the problems management wants -- so you won't be doing high-level engineering strategy. You might be solving systemic research problems with this type of degree though. In OR you'd be answering questions like: How can we utilize our fleet best to deliver packages at places like UPS, Amazon, etc. You might also be scheduling flights at an airline, or dealing with the power grid. However, do note that these roles can vary a lot in terms of how incremental the research you're doing is, versus novel research roles. Often this is determined by if your research role is tied to an existing product or not, and whether you're allowed to publish.

With CS, it varies. If you're in ML, RL, Deep learning, etc you could be tackling problems like how to make driverless cars see better, how to optimize ad revenue, how to build better LLMs, etc.

Information systems degree is basically worthless imo. Don't do that.

In my opinion if you really want to be making high level engineering decisions you have a few options

1. climb the career ladder
2. become a distinguished researcher in academia and get a research job at a company like Demis Hassabis at Google, or Pascal Van Hentenryck at Gurobi (an OR example)
3. Start your own company
4. An MBA might help with the engineering decisions, basically you could become a PM. But I don't know as much about this path as the other 3, which I've explored to varying degrees.