Seems “promptly” is still allowed, though I wonder why it was hidden.
Also, it’s peculiar that its word type is “noun, suffix” with no mention of “adverb”, yet the Patterns of Use section only shows it in the adverb form (i.e., 早々に and 早々と) and two of the three provided context sentences appear to me to be in adverb form. I think the hotel example shows it as an adverbial noun, but I’m not completely confident on my technical grammar recognition.
It’s also interesting that quite a lot of examples I found elsewhere use it in the suffix form (whether that be as a regular noun or an adverbial noun), but we don’t really see clear examples of that in WaniKani—particularly the regular noun suffix, if my assessment of the one example was correct.