The best place to look for this stuff is Emscripten itself. Its documentation can be a bit patchy but all the code is available to read so you can usually fill in the blanks.
I think the mem file mostly contains static data initializers, for all global variables in the C++ - including anything needed by libraries, class statics, and so on. That may or may not correspond exactly with statics in C# - if they are initialized by code (static constructors) then their values will likely appear in the code rather than as static data.