The t-test returns amongst other useful values the confidence interval on the difference between the means.
A CI on the difference of medians would be super useful to have for nonparametric tests like the MWU, so that not everybody has to comb through literature to figure out how to compute CIs for nonparametric tests.

I'm not entirely sure if for generic cases that'd require bootstrapping, or if closed-form solutions exist and robust enough.
A method to compute CIs for nonparametric tests is, i.e., given in Calculating confidence intervals for some non-parametric analyses, Michael J Campbell and Martin J Gardner, British Medical Journal 1988.