Hahahahahaha, yet another paper you don't understand, huh? Quick, point me to the part of the paper where they say you should test interactions by plotting predicted probabilities and seeing where CIs overlap. That's so dumb I can't believe I was even able to type it.

Not in the article explicitly, but it's common knowledge.

https://en.wikipedia.org/wiki/Confidence_interval

"Confidence intervals are closely related to statistical significance testing. [...] If the estimates of two parameters (for example, the mean values of a variable in two independent groups) have confidence intervals that do not overlap, then the difference between the two values is more significant than that indicated by the individual values of α.[16] So, this "test" is too conservative and can lead to a result that is more significant than the individual values of α would indicate. If two confidence intervals overlap, the two means still may be significantly different.[17][18][19] Accordingly, and consistent with the Mantel-Haenszel Chi-squared test, is a proposed fix whereby one reduces the error bounds for the two means by multiplying them by the square root of ½ (0.707107) before making the comparison."

Hahahahaha, wow, you literally couldn't find a worse passage to copy from Wikipedia for your argument! It literally says right there that what you proposed is "too conservative" and if CIs overlap, then "the two means still may be significantly different." Are you actively trying to embarrass yourself? That's my job!