Presumably instances of `MyObject` can be accessed by functions which are running while this function is suspended, waiting for the network call. It's single threaded, as in only one thing happens at a time from JS's point of view, but other functions can be invoked (by a request coming in, or a UI event etc) while an asynchronous operation is awaiting completion.

That's not true. You could return (either the promise being used or a directly awaited value) and that value would be made available through await / promise as well.