That ... is an entirely different question.
(and this is why I generally have been trying to focus my time on the full rules remaster project rather than addressing random Qs at this time - and I'm always happy to have volunteers to help with that btw! - but I was looking something up and stumbled across this thread so figured I'd chime in to hopefully help Zakath with passives, so hey, y'all got here me now)
My understanding is that when an action or effect must be implemented "immediately", it is done so .. right then. I mean, "immediately" is a fairly defined word in English, and probably the best word to describe the timing, but I believe that (while this isn't always the case with the designers' use of English language) the use of "immediately" in MeCCG is the same as the common English understanding of the word. When a card leaves play, its effects are negated "immediately" - not later, not after the chain finishes resolving, not after players have had a chance to respond, but "immediately" - to give just 1 example of 100s, literally. I believe this is consistent across ICE's use of the word "immediately" if you look at how the word is used (and thus this would be the clearest counter-evidence to how Zakath was approaching Anno 9a)... So to be frank, I'm not sure if you're trolling me, Konrad, or if this is an actual question!
If Slip Treacherously is played on Black Arrow, it doesn't tap the Arrow until the card itself resolves in the current chain of effects. When that happens during the chain of effects resolving, and the condition of "Black Arrow is tapped" comes into effect, the Black Arrow is "immediately" discarded at that time, before other actions may be taken, would be my understanding.
However, Ancient Black Axe is entirely different, because it doesn't involve discarding; it's a normal passive condition, not a 'discarding passive condition' per 9a. So as a normal passive condition, when Ancient Black Axe becomes tapped when Slip Treacherously resolves in its chain of effects, the condition of "Ancient Black Axe is tapped" comes into effect, and per Anno 9, the CC is added to the beginning of the subsequent chain of effects that immediately follows the Slip Treacherously chain of effects.
And by all means, you can not like blurred logic; just all of us being explicit about what the rules are versus our interpretations of those rules, and thus not further blurring the lines ourselves, would be my preference.