I'm not super deep into the game, but no, so far I've not noticed any jump scares. There was one little spot in the Office of the Mill that might be considered a touch towards that when the character hears someone approaching the door, but it wasn't in your face like a jump scare. The character spooked, and there was an accompanying dialogue box to go with it that I hadn't been expecting.
Mostly the game has been atmospheric mystery and clue collecting, but when present, there are weird gore elements such as dismembered talking heads, twisted parallel areas, and zombie-esque movements. I feel it definitely plays more on psychological horror elements and the anticipation of what comes next, rather than a red paint budget.