I think what is happening is that your specification basically implied that mu is definitely, nearly 100% guaranteed to be very close zero. But how closely each alpha was to mu wasn’t nearly as certain (i.e., tau[1] was allowed to vary). So your posterior still indicates that mu is basically zero (because that’s what your prior implied) and the data pulled each alpha up toward the empirical mean(s) of each respective school’s df['MathAch']. But I just skimmed through quickly, so I may have missed something.
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