On reading more about it, I realize you are right that they were/are rarely paid by journals, but it used to be a prestigious part of your academic career, so it fit in as a normal and valued part of your research work, while being paid by their university or institute or whatever.

In fact, there are platforms that allow authors to pay to have their articles reviewed, but this is felt to be not gaining traction because the researchers' bosses consider it moonlighting instead of an essential part of the common work of advancing scientific knowledge.

I know in the 2000s my research advisor asked us to analyze papers and replicate methods and measurements from other groups on occasion, sometimes because he was a reviewer and sometimes just because it developed specialized skills in our field. We (and he) only worked so many hours each week, regardless it was research or review, and were paid a stipend/salary so we were all definitely getting paid for our time. The key was that the university "allowed" us to spend time on this sort of community service/professional development, by which I don't mean they really closely accounted for anything, but just didn't have a breakneck publish or perish vibe.