The process is actually much easier than you probably think, based on Rubin's approach.

You average the estimates from imputation based analyses and that gets you the estimate value across imputes.

Then the SE within and between imputations based analyses values. The section in your link about single pooling covers this. So the estimate is super easy to get, then you create the SE based on within and between imputation variability. This makes the SE measure a little larger since it takes into account the slight variability accounted for between imputes, since it is probability based.