I tried searching around a little more. It seems the word for ‘rite of passage’ (which is the sort of thing for which there is a ‘postliminal’ state) is 通過儀礼, and so, if you search 通過儀礼 局面 (‘rites of passage phases’), the first two results seem to discuss 分離, 過渡 and 統合 more than 境界.
It would seem those are the terms for the different phases that have become accepted in academics, probably because they’re slightly more descriptive than one’s position relative to a 境界.
閾 might still be workable, and you would probably form related terms by replacing 境界 with 閾 in the phrases Leebo gave, but it would translate the metaphor of ‘liminality’ into Japanese, since limen means ‘threshold’ in Latin, which may not be as easy for those new to the subject to grasp. Plus the fact that it is a rather rare kanji. It can be used for the idea of ‘threshold’ in a figurative sense: 閾値 means ‘threshold value’ in biology and psychology. However, the reason (I believe) 分離, 過渡, 統合 and 境界 became more popular terms to refer to the concepts proposed by Victor Turner and his predecessor van Gennep is just that the words are more descriptive/intuitive. It’s also possible that the metaphorical sense of 閾 isn’t very strong in Japanese, because in the dictionary, I only see it for technical terms that relate to biology and psychology.
Additional thought: Ultimately, it probably has to do with with the translations chosen by those who first translated Turner and van Gennep’s ideas into Japanese. It might have happened as part of a wave of importing Western ideas into Japan, which would have encouraged the translators to make the concepts as easy to understand as possible so Japanese scholars would be able to use the ideas themselves.