I am not familiar with Hercule Poirot, so I can’t speak to how closely it fits in that regard. I enjoyed the story; it’s something that can stand on its own instead of needing to already know the characters. It had a very cozy vibe to it. The stakes felt fairly low, but it still felt good to solve the puzzle and figure out the correct answer.
There were a couple of points where I think it would have been nice if there had been a little more description. For example, when I wrote “Listen to Poirot” near the end, it might have been nice if you had talked about something like the sound of him cooking dinner instead of “I heard nothing unexpected.” From a gameplay point of view, “nothing unexpected” is a good way to convey to the player that this was unimportant and made sense; from a story telling point of view, I would have enjoyed that little bit of extra immersion.
I think you did a good job with this.