Once again, Jentz’s Panzer Truppen is a good source.
There were a lot of StuG's in Italy, prior to the Salerno landing. 16.PzDiv had 40; 24.PzDiv had 42; Herman Goring Div had 16 StuG and 6 StuH; 3.PzGrenDiv had 42; 29.PzGrenDiv had 38.
All, as of August 1943. Later, in early 1944, reinforcements of Pz Abt (Fkl) 301 brought in another 30 StuG's. Specifics for the replacement units from 16.SS-PGD was not given.
Jentz states by Jan 1944---there were 138 StuG, in Italy. 160 total Pz IV (läng).