If I create a barplot using Seaborn and specify the geometric mean or the median as the estimator, does Seaborn know to use the appropriate standard error formula to create error bars?
This information is in the documentation of Seaborn.
They show a bootstrap confidence interval, computed by resampling units (rows in the 2d array input form). By default, in seaborn version 0.8.1 it uses 95% of confidence interval, which is equivalent to a standard error. This value is a parameter that can be changed.