Expectation maximization (EM) is usually applied to posterior marginal mode finding problems. This is not a mean. Posterior modes and max likelihood estimates only have nice properties asymptotically in well-behaved models, where they converge to the true value.
Bayesian posterior estimation typically uses means, which minimize expected squared error, a strong staistical property in finite samples. Using the posterior median gives an alternative point estimate the minimizes expected absolute error.
Stan doesn’t disambiguate means—only Stan plus a model does something. If the model is continuous and differentiable, Stan’s likely your best bet for fitting.