"Publish or perish" in this sense is 100% only applicable to very modern academic life. Arguably it really only became a meaningful statement about the pressures on most faculty in the 1970s into the present day.

The earliest point where you could identify any strong professional pressure to produce research outputs would be after the establishment of the "German model" research university, the first of which in the United States is commonly thought to be Johns Hopkins University in Baltimore in 1876. The "German model" research university emphasized the importance of scientific and social scientific research as well as philosophical and artistic inquiry for its contribution to the nation-state and the national economy. But even in the case of these actual German institutions such as Heidelberg University, they only took shape in this way in the mid-19th Century despite in many cases having been in existence since the late medieval or early modern period.

University faculty prior to the 19th Century did not face any particular expectation that they would publish written scholarship or conduct major research projects. They were expected to have deep erudition, certainly, and faced other kinds of possible threats to their position (unpopularity with students, who often paid tuition to support specific tutors; rivalry or unpopularity with other faculty or heads of schools; heresy or religious unorthodoxy during the Reformation or before, public enmity with a rival intellectual with political support, etc.) University teaching was a considerably more peripatetic or itinerant affair before the 19th Century, and even into the 19th Century, many institutions in the US and Europe that are today regarded as very prestigious found themselves at time desperately scrounging for enough faculty to teach.

It is really only after 1955 in the US that faculty at large research universities began to feel serious competitive pressure to produce research, and even there, that was blunted considerably by the twin demands of the GI Bill and the Baby Boom, e.g, universities were suddenly awash in new students and up until about 1972 or so, that meant that it was remarkably easy in relative terms to obtain a university position if you had the basic credentials (a Ph.D, essentially). This was also the golden age of tenure, adopted increasingly as a response to abuses during the McCarthy era, so the faculty hired during this time often were relatively protected from rising demands for research outputs in the US, UK and elsewhere. (This has been a point made by Peter Higgs, for whom the Higgs boson is named, among others: that faculty were free to be productive or to pursue basic research as they saw fit in that era but would by later standards have been unemployable.)

In the mid-1970s, the academic job market, especially in the humanities, collapsed as the GI Bill and Baby Boom waves cleared their university education and early forms of austerity began to be imposed in public universities especially. The somewhat predictable consequence of this was that competitive pressures on incoming job candidates rose dramatically, and this is where "publish or perish" acquired its initial bite--a situation which continues today despite the ongoing casualization of academic labor.