It’s kind of funny that your way of dealing with branching narratives of this type is to play through only once and treat your path as canon, since the norm (at least in VNs, which are generally shorter and contain fewer mechanical challenges) is to get 100% completion (to the extent that, in many games, the ending the creators consider ‘canon’ doesn’t even become unlocked until all the ‘normal’ paths are visited — see Everlasting Summer, for example, whose core plot is only vaguely hinted at until you slog through all the formulaic dating sim BS, or Sharin, which does something similar by unlocking whole new dimensions of meaning in throwaway lines from previous play-throughs in what is essentially an easter-egg route that nevertheless is necessary to play through in order to get completion).
I wonder if triple-A games, because of play time and budget and aspirations towards ‘cinematic experience’, don’t play this way — but games focusing on branching narratives as their primary or sole mechanic are often built with the assumption that players will engage with multiple routes, and reflect this thematically (with plotlines involving time loops, time travel, alternate universes, and so on — everything from Steins;Gate to Higurashi does this). This is a very different way to engage with a game. It’s not precisely leaning on the fourth wall, but instead, taking greater advantage of an already existing mechanic for thematic reasons, telling a story that is much more difficult to tell in non-branching media. (There are attempts to tell this kind of story in film. Run, Lola, Run, for instance, or Tatami Galaxy. They feel more like formal experiments than direct experience because the choices aren’t directed by the audience, and this detracts from their effect; less competent attempts are even less memorable because of this.)