I don’t really have an example that you can check out (unless you read Polish), but the first Polish RPG: Oko Yrrhedesa (written by the author of the Witcher books) does something like that.
The original game (later, the first chapter in the printed version) is written all in prose walking players through the whole idea of roleplaying, from how to imagine the world to dice rolls (the text also worked as an intro to RPGs in general).
It starts with players sitting around a table IRL, the narrator says how they are actually in a fantasy tavern - describing the sights, smells and people. Suddenly a sound (I think a car outside) pulls them back IRL and that shows how you use your imagination to play (it works surprisingly well). When we get back to the fantasy world, we follow the characters on a simple quest.
The book works by showing the players “roleplay the right way” throughout the story. So when they are hurt, they say so, and not “I lost 4 HP” and then the narrators says why this is important to stay “inside the narrative.” Honestly I love this approach - it works great in introducing the idea of RPGs and makes the system easy to understand as you see it used in context. I was toying with the idea on making an intro game in this style, but other projects took precedence. So I am really excited for your game, and I am happy to help.
I did a read through and comment on twitter about the game - it doesn’t go too in-depth, but maybe you can find something helpful there. Feel free to ask questions on here if you want to know more about any aspect of the game… and if you can’t find any other examples, I can try doing a quick translation of the chapter (it is around 20 trade-paperback sized pages) so you can see how that flows.
What is your game about?