It seems that "transsubjective" means "across subjectivities" in the sense of not necessarily being restricted to any specific individual(s) (e.g., may include nonparticipants), while "intersubjective" means "between individuals" and also entails the ability to take the other person’s position. In that case, the reference to “intersubjective understanding about things and events” posits that persons actually involved in a situation have a capacity to reach mutually insightful and empathic understandings among themselves.
That capacity is contrasted, here, against a "capacity for decentered perception and manipulation of things and events." If my understanding of Piaget is correct, the concepts of decentering and internality, which were borrowed from him (p. 14), refer, respectively, to the ability to take the perspective of another person and the transition, in the developing child, from external (physical) to internal (mental, symbolic) representations. Here, however, Habermas evidently wants to construe decentering, not as evoking anything resembling an increased capacity for empathy or interpersonal insight, but rather as enhancing one’s ability to take an objectivist, impersonal view from nowhere.
Internality, in this context, seems to mean, not Piaget’s concept of developing ability to engage in mental manipulation of symbols, but rather that which is seen through the eyes of the participant as distinct from an outsider’s perspective. Alternately, the reference to "internal relations" may mean to emphasize "relations," not "internal"; that is, the point may be that decentering and manipulation are related to a capacity for intersubjective understanding -- that, in other words, development of an objectivist perspective toward the world results, not merely from highly individualistic interactions with things, but also as a result of a social or community context.