The Polish book
Wydawnictwo Militaria 258: Panzerabwehr Artillerie (publ. 2006) features a table that shows ammunition production for German anti-tank guns during WW2 – including the Pak 97/38:
The ‘HL’ refers to HEAT. ‘SpGr’ is HE. I think the ‘PzGr 40’ is AP.¹ Using these definitions the total production of ammunition for the Pak 97/38 was 2,812,700 HE, 2,581,900 HEAT and 1,394,100 AP. The HEAT figures match those quoted by cbo.
I doubt whether the Germans palmed off all of their AP rounds to their allies. The captured technical data sheet I posted earlier shows that they were using them in the Summer of 1944.
¹ The Polish book describes the Pak 97/38 ‘PzGr’ round as ‘przeciwpancerne’ – which I think roughly translates as ‘anti-tank’.