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This is actually specific to mathematics. You are welcome to share about other fields.

Question is as mentioned above.

How many diagrams is too much in a research article?

Do more diagrams annoy a reader?

That entirely depends on the article itself. In some cases diagrams aid an explanation and make it clearer. In others they offer little insight. If an article depends on having many diagrams of the former kind, then I don't see that "too many" is an issue. But even a few of the latter kind may just get in the way of understanding.

Words and pictures can be complementary. It is a judgement call by the authors as to which is best in a given case. They may err a bit, but that is human nature.

In general, think about whether words or pictures/figures better convey your meaning and act accordingly. Sometimes both are needed. Examples illustrating (note the word) a concept are often best presented in figures. Imagine a Calculus textbook without figures. Now imagine one without formulae. Would either work?

I looked at 5 papers of mine in experimental science. The results:

As you can see, it's about ~1-2 figures per typeset page. I did count "panels" (a), (b), etc. as separate figures even though not numbered that way as they are separate on the page.

I never got any push back or even questions on figures from journals or reviewers. Had one co-author on D ask me to pull 3 modeled regressions (or number would have been higher). But the objection was not visual impact but just that he disagreed we needed to show a negative relationship.

In terms of what to show, they were almost all just data graphs and are in the results section. Maybe once or twice I showed a "cartoon" in discussion. Intro, methods, and conclusion tend to be figure free. So the figures are concentrated in the middle of the paper.

I really never wondered what to show--felt intuitive.

I suspect there will be a practical limit related to experimental/theoretical sciences. You should also consider how peers start to read an article. This will vary a lot, I will often read the abstract first and then take immediately a look on the figures, then, maybe, I switch to conclusion, then, maybe, I start from the introduction. If your results are important and understandable easily, your paper will become cited many times in any way and peers are more inclined to read it, if you present a new method as a unknown researcher, I would apply a poster strategy and think thoroughly about what the 1-2 key statements/messages are you want to present instead of bombarding the reader with redundant figures. The attention span you get is the unknown parameter. Basically, there should be not much redundancy in your paper, therefore the the data/figures IMO should be compressed as much as possible withoug looking cluttered. This is an art and science you have to practice and you should carefully analyse how it can be improved whenever reading other papers. Asking how much figures are too much is leading away from the key problem here, which is attainable attention.