Just wanted to add to have a game that reacts to your options, without completely branching the story, is really a tall order, and I understand why authors may be compelled to avoid it. Efficiency wise, it's inefficient to multiply the possibilities and have the game rigged in such a way that each player, according to specific choices, will experience different scenes, or different variations. I multiplies the work for the same amount of gameplay that each player gets. A simple branch-out, while creating two linear stories, keeps it simple. But, arguably, less interesting!
Like you say, many games fail to avoid the pitfalls of writing a story where choices don't seem to matter, the MC's characterization is completely flat, non dynamic, because they can do whatever they want, without impacting the outcome. Even FL branches out eventually, although I think they did a good job keeping most of the ending-locking choices to the late game. Sandbox games might be better at this, adding flags with an expiration timer, so that if your choices are witnessed, they affect your reputation and people's reactions to you for some time, but can be removed later. A dramatic example of this is Girl Life, where you have a pair of events that can cause the MC to be dubbed a slut and have their reputation ruined for a long time - but if you commit to it, you can restore it throughout the game. It just takes a full school year to do so. Dynamic stats may also help - a perfect example of this is Friends of Mine, where you have a feminisation stat that, once over a threshold, makes you a sub in most encounters, but it's dynamic and you can try to balance it so that you can go back and forth. You can still argue that it "flattens" the experience, and that it feels gamey in that one moment you're treated like a sub, the next you're treated like a dom, and all it takes you from going from one to the other is choosing to masturbate one way or the other. But if you abstract from these mechanics, you can easily choose the way you want to play: make all dominant choices and you remain a dominant character, make all sub choices and you become, and remain a submissive character. True, there's a particular story arc where you can be railroaded into one path, but you can also avoid it through choices, and even if you don't, you can still steer your character as one who's resisting what others would force upon them. Quite a good one.
Would love to know which games, if you're willing to share. F95 tags are arguably the best around, and the ability to combine them is great, but it still feels like there's a lack of nuance. That's probably inherent to tags. And then, you have games that fail to get all the tags that should apply to them ("hidden gems") and those that get tagged "defensively" despite their content having very little to do with said tags.