Correct, my initial description of the intervals was for equal-tailed intervals, which HDIs are typically not (but are sometimes!). But worse than that, there are many HDIs (intervals that include N% of the mass) that are not equal-tailed. The arviz hdi function returns exactly one which is the HDI with the minimum width. There are also issues once you are dealing with distributions that are mutlimodal. The bottom line is that saying you are presenting “an HDI” doesn’t really indicate what you have constructed (or how).