Katherine's default walking speed is very slow, designed to encourage careful observation. However, for covering longer distances or backtracking, holding down the R2 button (or Left Shift on PC) will significantly increase your movement speed. This isn't a true 'sprint' in the action game sense, but it's a faster walk that becomes essential for efficient exploration.
Don't be afraid to use it frequently, especially when traversing between major locations. You won't miss any crucial narrative triggers by moving faster, as light anomalies and interactable objects will still become apparent as you approach them. It simply makes the journey less tedious without compromising the narrative experience.