Ref. No. 1013/41-263
In the name of Allah the most Gracious the most Merciful
The answer to your question is as follows:
As you have written, it is not in the current versions of Mustadrak. I also searched and could not find it. However, ‘Mulla Ali Qari’ wrote in ‘Mirqatul Mafateeh’ with reference to ‘Mustadrak’ with the addition of 'علی'. So it could be read both ways (with or without 'علی'). Allama Nawawi has also declared it in ‘Azkar’ as Sunnah to recite Bismillahir-Rahmanir-Raheem and Bismillah in the supplication of food. So there is an extension in this matter.
And Allah knows best
Darul Uloom Waqf Deoband