I agree. Oftentimes, branching storyline games tend to be weak in execution.

It ends up being either (1) the same story with 3 slightly different endings or (2) three completely different stories, supposedly linked together.

I think the best executions of this genre try to do something creative with the storylines and tie them together. If Alice does something in storyline A, perhaps when we go down storyline B in the future we’ll realize why Alice did what she did, etc.

Much stronger similarity is found in the "Visual novel" style games, although those are not so popular in the US. That also they have been to some degree influenced by the CYAO book format seems plausible.

I'd say they used to be unpopular in the west, but that's changed. See https://itch.io/games/genre-visual-novel for a sampling of games that are mostly made in the west, as well as Russia and Southeast Asia.

You might enjoy The Stanley Parable game if you haven't tried it already: https://m.youtube.com/watch?v=fBtX0S2J32Y there's a free demo and they're working on an "extra deluxe" version now

I actually absolutely adore TSP, and I realise that it has different endings but I feel like it is fundamentally different from "branching narrative" game, although now I think about it I can't quite put my finger on why...

The sort of thing I hate is GTA IV style, Kill X or Kill Y "choice moments". Quantic Dream games are essentially nothing else, it really annoys me when people suggest those games are somehow the most mature and "artistic" games out there, when to me they are basically bad CGI films.

“Choice moments” like you describe here are basically single lane roads becoming two-lane roads. The reason these are so common in gaming are because of the high difficulty of producing true branching. Even the CYOA branded books suffer from this difficulty. However, branching narrative can definitely work. Most collaborative storytelling games (the “not on rails” subclasses of “D&D”) are almost by definition branching narratives. It’s both the social element AND the endless possibility of collaborative storytelling/invention that make those games so successful.

Video games have a higher barrier to accomplishing this feat. Imho simulations like The Sims, CDDA, or Dwarf Fortress are able to accomplish it best.

I thought both Until Dawn and The Wolf Among Us were really enjoyable, although Until Dawn branches a bit less than a first play-through might lead one to believe.