I enjoyed reading this, and Runecairn core rules! Together, they adapt Dark Souls mechanics and level design very well and have a nice atmosphere. If you're familiar with Dark Souls, many of the encounters feel very familiar, but as a player, I still might have fallen for the tricks and traps the first time facing them.
The combat system is faithful to the spirit of the Soulsborne video game series but I think you need to have played the game to get a sense how it's meant to look and feel. And if you've played the game, it's hard not to be reminded of the specific mechanic or part of a level or story that Runecairn/Beneath the Broken Sword takes inspiration from, which can be a bit jarring.
Regardless, as a starter adventure for Runecairn, Beneath the Broken Sword really works. It teaches the player how to play the game, and the Warden how to design new levels. It's compact, to the point and well written. The layout is good, and in keeping with OSR+ design philosophy. Reading the PDF, I would have hoped for a minimap for each area to avoid scrolling back to the map page.
A lot of RPG folks like me are trying to work out how to make our favorite fantasy action rpg into a tabletop version, and Runecairn showed me how! Runecairn and the starter adventure should definitely be read and purchased together.