Were predatory journals widespread before publishers of reputable journals introduced the "author pays" model? After reading yet another news article about predatory journals/conferences and how they weigh on the finances of labs in some countries, I started to wonder the following. Were they widespread before publishers of reputable journals started introducing the model where the author pays to have their paper open-access, the so-called "gold open access" (a name I dislike very much, but that's not the point)?

Indeed, I would expect that before that (which seems to be a relatively recent development, maybe less than 10-15 years ago...?), labs would have been much more reluctant to pay for the publication in a predatory journal, because that would have been a surefire way of telling that the journal was junk. And if a researcher had to pay from their own pocket, then I would expect the practice to be much less common, simply because fewer people could afford it.
Anecdotally, a significant proportion of journals on post-Soviet space in 90s were quite happy to publish literally anything as long as author covers the "publication costs". The peer-review was either very light or non-existent (e.g. authors could invite their friends to act as a referee). This was used by some high-rank officials to secure the publications required for their academic degree, which gives a bearer a certain level of prestige even if they never practice science.

This happened before any OA was introduced in Europe/USA and it is still happening now. The existence of predatory journals is probably more driven by the publish or perish principle, than by OA.