I got out, but with a bunch of puzzles unsolved. I didn’t brute force anything or do anything out of expected order. Maybe this is the framework for a more complex/lengthy game later? Anyway, it felt weird to get out knowing there were things left uncompleted.
Edit: I found a walkthrough and see what happened now. Instead of using the extender hand to grab the power cord, I took the crowbar from the can. That lets you jump a whole pile of steps&puzzles and get out.