Found a way to clip out of this part in Contractual Obligations (happens around 2:10 in the video). Haven't gotten further than this in the game so I don't know if it's useful, but you can explore the entire next area as well as slide past the fire walls in some corners. Don't think any cutscene triggers load like this, since I looped around the whole area and only triggered a short cutscene when I entered subcon forest.
Basically if you have the no-bonk badge and dive into a sloped surface that you can't climb up, you can carry your momentum until something stops you. As per usual, if you get stuck in the sliding animation it'll teleport you back to your last standing point. In this case, it warps you out of the contract room. The particular setup I've had success with is to jump off the contract, then wall-climb, jump off, double jump back into the wall, and then dive.