In my (perhaps unpopular) opinion: you either do this through puzzles, or you do this through narrative branches.
I feel like I have zero interest in narrative branch-based IF, though I know this sounds like such a sweeping statement I remain open to having my mind changed. But when I try a game like that I just have zero interest in making those choices, I don’t get what kind of headspace I’m supposed to be in: do I pretend to be this character and then try and think what they would do in that situation? Do I think what would I do in that situation, even if it’s happening to a character in circumstances very different to my own? Is it supposed to send me into some ethical conundrum, even if I know and I don’t mind knowing this is happening to letters on a screen and won’t affect any real living creatures? Any games I’ve played that are based on “you get a different path/ending based on your choices” to me just turns into a gruelling mechanical exercise of trying to hit every path, i.e. it becomes puzzle-based but like, a really boring puzzle.
Puzzle-based is still interactive, because you have to figure out how to act to move the story forward. IF like Photopia gets called “puzzleless” but it still operates like this. Even Rameses operates like this, thought it takes that logic and subverts it by ignoring your attempts at solving puzzles and moving the story forward without you, in order to remove your agency - it still works with an expectation of agency that I think is more typical of puzzle-based than branch-based IF.
Clara Fernández-Vara’s PhD thesis is a really interesting exploration of how puzzles work to create interactive stories in noun + object adventure games