Also discussed by Maharal in Gevuros Hashem end of 51
Indeed,
.. hagadas shlaima from R Kasher is a good mareh makom
Hu Shata can also be a contraction of הא שעתא or הא שעה. So the nikkud doesn't necessarily give it away.
(There are those who say at the end of achienu the proper term there is hu shata; as well. There the order of hasta ba'agala ub'zman kariv would need to be explained. )