The term, systems engineer, had different interpretations depending upon the environment and context. In my experience, in IT the term could be better describe

The term, systems engineer, had different interpretations depending upon the environment and context. In my experience, in IT the term could be better described as systems integration, i.e. building systems out of sub-systems. I have engineering degrees and decades of experience and yet I wouldn't claim to know more than a fraction of what you allude to in your question. Very loosely speaking there are there major areas of systems engineering, mainframe based, large-scale Windows enterprise server based and Linux cloud based. The technologies differ greatly across these so you probably should choose a single area. The common ground amongst these three areas is network engineering. Any large scale environment comprises complex interconnection of nodes, switches, load-balancers, etc. If I were in your shoes, I would find a job with a medium sized systems integrations consultancy and then develop my skills in one area at a time. Over time you would end up with a comprehensive knowledge across the many areas.