I did 100 encounters (during the day), and out of those, I got 80 Stakataka, 2 Heracross, 8 Buneary, 6 Trumbeak, and 4 Zoroark. Based on this, Stakataka's encounter rate is around 80%, but this of course could change if I were to do more attempts. Around 80% seems accurate to me, as it's high enough that you're getting stakataka/blacephalon nearly every time, but it's low enough that other encounters feel possible. This isn't an answer, just an observation, and it wouldn't surprise me if the encounter rate were even higher or slightly lower.