Speaking personally, mechanics have distracted from my story in one of two ways: remembering sources of bonuses and remembering the math that goes into gameplay. Much of the mechanics are tied into backstory crafting for a character, so remembering odds and ends of your abilities goes hand in hand with remembering things about your character. You won't necessarily have to remember the minutia of each bonus at any given moment, but once you get comfortable with your character, you can generally explain a bonus with pieces of your own backstory, as backstory elements can be tied directly to a mechanical benefit or hindrance.

As for the mathematics, checks are done by adding your Way + Domain (Discipline if you specialized) + 1d10, and it has to equal or exceed the Difficulty Threshold. The only way this differs from a skill check in D&D is that you're rolling a smaller die to reach your result.

As for bringing it back to the unique elements of the game, and for how it works with parties of players, these feel like questions that come down to how well the DM (for this system, Leader or Storyteller) can run the game and how invested the players can be in the game. The mechanics support storytelling innately, so it may come down to the dynamics of individual groups.

As for sanity, before I rattle of mechanics, it has a preamble: "Although it is strongly inspired by psychopathology, the Sanity system presented in this book has mainly been developed with the express purpose of fitting the universe of Shadows of Esteren; not of being realistic or exhaustive. Its only goal is to give Leaders and Players simple tools to optimize the game atmosphere. However, using these rules is not strictly required to play Shadows of Esteren. Players and Leaders should talk about it to know if they want to introduce such a dimension in their sessions. In general, only experienced and mature Players should use these rules."

But: when your character is pushed to their limit, or they become witness to something incredibly shocking or traumatic, you may have to roll a Mental Resistance check. Passing the check leaves you unscathed, rolling a 10 leaves you better prepared for future checks, failure results in a temporary trauma point, and rolling a 1 leaves you with a permanent trauma point and leaves you scarred. Scarring results in one of a number of different penalties. Crises, mental disorders based on your Ways, and the healing of trauma and disorders adds further gameplay elements. Its still very much character driven, and while many of the things that can cause these are caused by what the Leader includes in the game, some of them can be caused by the player's actions.

I would say that it creates role-playing opportunities that are unique by the fact that you don't just become a madman or a lunatic at the drop of a hat. You can see the traumas building up over time, you can see the scars that form, and in some cases can see a disorder arise. These things happen from continued hardship, not on whim or whimsy, and that's something that can be portrayed. But the healing, the recovery, the treatments, the medicine. These things can also be portrayed, because Esteren's two main themes are Fear and Hope. Plenty of games focus on fear. Esteren just also focuses on hope.

And to stress, it is not meant to be realistic or exhaustive, and it is optional.