My impression of semantic shift is the evolution of a word or term so that it is significantly different in meaning from the original sense. If that is the case, program, either as a verb or a noun referring to the operation of a computer, has not strayed far from the meaning attributed to the word since the 1800s.
According to etymonline.com, as a noun, program is derived from
1630s, "public notice," from Late Latin programma "proclamation, edict," from Greek programma "a written public notice," from stem of prographein "to write publicly," from pro- "forth" (see pro-) + graphein "to write" (see -graphy).
General sense of "a definite plan or scheme" is recorded from 1837. Meaning "list of pieces at a concert, playbill" first recorded 1805 and retains the original sense. That of "objects or events suggested by music" is from 1854. Sense of "broadcasting presentation" is from 1923. Computer sense (noun and verb) is from 1945. Spelling programme, established in Britain, is from French in modern use and began to be used early 19c., originally especially in the "playbill" sense. Program music attested from 1877.
While the computer sense is listed as beginning in 1945, a computer program is a definite plan or scheme for the operation of the machine. That type of usage goes back to at least 1837.
Similarly, etymonline.com describe the verb derivation
1889, "write program notes;" 1896, "arrange according to program," from program (n.). Of computers from 1945. From 1963 in the figurative sense of "to train to behave in a predetermined way." Related: Programmed; programming.
Again is suggests computer usage beginning in 1945. However, in 1889 program is used to mean write program notes which is what a computer programmer does. The meaning arrange according to a program from 1896 also seems pretty close to modern computer programming activities.
This sounds like old wine in new bottles.