What is the simplest operating system or platform upon which we can do Software Engineering in this day and age?
One of the main activities in Software Engineering is conceptual software design, and making concepts for a software does not necessarily require a specific platform. It can be done with pencil and paper, by drawing UML diagrams, data models or flow diagrams, or just by writing down a concept in textual form, making no assumptions about operating system and platform.
Maybe you meant your question in a different sense, like
"what is the simplest operating system or platform upon which we can run actual programs produced by a Software Engineering process"
but then the answer is: Software Engineering can be done for "any platform which is capable to execute programs", pick the one you think is most "simple" according to your personal definition of "simple".
To be fair, there is more in SE than just making concepts for software. For example, this site puts the focus on all activities of the systems development life cycle except coding issues. But as @BasileStarynkevitch correctly wrote in his answer, SE activities for "small systems" are typically done by using a separate, bigger development system and a cross-development kit. So SE activities like configuration management, versioning, testing, QA or writing documentation, can be done on a standard PC with an OS for which a matching dev kit is available. That makes it possible to do all kinds of Software Engineering activities for virtually any contemporary destination platform.