Origin of the biochemical term, Pi (inorganic phosphate)
This terminology is at least as old as September 1944 when Enzymatic Synthesis of Acetyl Phosphate Journal of Biological Chemistry
155,  55-70 was published by Lipmann, which says:

Inorganic phosphate, referred to as Pi, was estimated
colorimetrically

See also the definition of &quot;inorganic phosphate&quot; and &quot;orthophosphate&quot; from this 1943 University of Wisconsin Thesis:

Compound:  Inorganic phosphate or orthophosphate
Definition: Phosphate whose calcium salt is insoluble in water-alcohol mixtures under the conditions to be described. E.G. NaH2PO4

In other words, &quot;orthophosphate&quot; was a generic term for mono, di, or tri basic phosphate.  It did not have the narrower meaning attributed in the OP.