I also have the same questions. I looked at the source code and yes ArviZ is computing the HDI correctly, but then the potential issue is in the names as noted by other users. Here is the relevant code:
hdi_post = hdi(dataset, hdi_prob=hdi_prob, multimodal=False, skipna=skipna)
hdi_lower = hdi_post.sel(hdi="lower", drop=True)
hdi_higher = hdi_post.sel(hdi="higher", drop=True)
metrics.extend((mean, sd, hdi_lower, hdi_higher))
metric_names.extend(("mean", "sd", f"hdi_{100 * alpha / 2:g}%", f"hdi_{100 * (1 - alpha / 2):g}%"))
So if you plug in the default value hdi_probe=0.94, then alpha=0.06 and you get the names hdi_3% and hdi_97%. But why are they doing so?