The Atari ST operating system used .APP as well. This was in 1985.
.app was rarely used though. Most things used the .prg extension.
Oh that’s a good point you have there and app is just an abbreviation of Application which I think philosophically was a subset of Programs / Programmes.
It's always Program; in British English Program and Programme are not interchangeable and mean something quite different. A Program is a piece of computer software, a Programme is a series of planned events or a sheet of paper/booklet listing a series of details about an events. That we use the two distinctly is pretty powerful and the ambiguity of using one spelling is removed.
NeXTSTEP was around in the late 80s, came out in 1988.