Thanks for the tip. The behavior actually seems to depend on std::cerr/stderr.. when stdout is used instead then the stacktrace is gone (i.e. works also in C).
To then also get rid of the annoying "source file" info console.log has to be replaced before the EMSCRIPTEN Module is instanciated, i.e. putting something like the below into the respective file does the trick (and it doesn't seem to have any negative effects on the scenarios where you actually want to log an error with stacktrace):
let origLog = console.log;
console.log = function(t) {
setTimeout(origLog.bind(console, t));
// "lose" the original context
};
problem solved :-)