[Chris Reinders Folmer]

I do not recall all the details but in the multiple imputation framework, the degrees of freedom depend on the within and between imputation variances. These variances are probably different for different sets of variables. The Methods and formulas in mi estimate provide details.

I think you are correct. This is from the manual:

Finally, mi estimate reports a coefficient table containing the combined estimates. Unlike all
other Stata estimation commands, the reported significance levels and confidence intervals in this table
are based on degrees of freedom that is specific to each coefficient. Remember that the degrees of
freedom depends on the relative variance increases and thus on how much information is lost about
the estimated parameter because of missing data. How much information is lost is specific to each
parameter and so is the degrees of freedom.

[Richard Williams]

Here is yet another approach, that I suspect would be quicker than reshaping and hopefully give the same result.

use "C:\Users\rwilliam\Downloads\2sample-IV.dta", clear
ttest hscore = wscore
mean hscore wscore
testparm hscore wscore, equal