I am a professor in a mathematics department at a state research university (University of Georgia). We do not have requirements on the publication rate (or record) of our tenure track faculty, but we have some informal expectations. Two or more papers per year is pretty good. Less than one paper per year is not so good, unless these papers are exceptional in quality: in mathematics, the very top journals are so elite that the majority of lifelong research mathematicians never publish in them.
On average, a postdoc has a lower teaching load than a tenure track job, and even when the numbers are equal, postdocs mainly teach less demanding courses. (For instance, several of our postdocs are currently teaching two sections of first semester calculus. I am currently teaching undergraduate real analysis and graduate algebraic number theory.)
So the following conclusion seems reasonably inexorable: if you wish to attain a job as a tenure-track professor at a research-intensive institution, you have to show during your postdoc that you can attain the quantity as well as the quality of research that will be expected of you in that tenure-track job. Many postdocs are still finding their research footing and, in some cases, really just beginning doing their research in a largely undirected way. Such people may not be putting out multiple strong papers a year. But I can assure you that the tenure track job interviews are full of postdocs who are hitting those marks.
In 2022 an assistant professor of mathematics is not really a "journeyman" who is just starting to do business for themselves; rather these are people who already have a research program with some successes in their rear view mirror. To get to this point takes time, and as mentioned in another answer, multiple postdocs totaling 4-6 years are becoming increasingly common.
I do want to end by mentioning that we are also not looking to hire people who are in the practice of writing papers just to have publications. If half of your publications are in journals that are not especially reputable (or worse, conference proceedings or other venues where the rigor of the peer review is less than clear), you will not be an attractive candidate.
It's a competitive world out there, for sure. Good luck to everyone.