I’ve only played through once, so I don’t have any first-hand experience of how much branching there is. But in the Disco Elysium thread I posted a summary of someone else’s playthrough I came across, and it was very different to what I played, and in surprising ways. Any details would be spoilers, but I’d also assume the branching narrative is a large part of the point of the game.
Whether there’s more than one tree’s-worth however, I couldn’t say.