Read the source and modeled the loop instead of just tapping through: one button, hold to brace, release to breathe. The bones are good, and scheduling the pulses randomly (gaussians, no fixed pattern) dodges the memorize-the-timings trap that sinks most one-button timing games. No line to learn. But the threat isn't real yet.
I ran your exact update rules over 8000 nights in an offline sim, with a bot doing the dumbest thing possible: hold the button forever, never release once. It won 100% of nights, and the door's worst opening across all 8000 was 0.33 of 1.00. Stamina does empty (~29 times a night), but each exhaustion only drops brace for about 0.8s, and openMeter gains at gap*0.62 while it decays at 0.30/s, so no exhaustion window ever gets the door past a third. Net: "let go to breathe" is optional. Never letting go wins every time. The stamina bar is decoration.
The fix is in your own flavor line: "It pushes when it thinks you are tired." Make it true. Add a term like push += max(0, 0.40 - stamina) * 1.8, so a spent body is exactly when the hall leans hardest. Re-ran the same bot: always-holding now loses 100% of nights, while a policy that releases to refill and braces through the pulses wins 100% with the door peaking near 0.36. Same code, same feel, but the breath becomes a decision you have to time instead of a ritual you can ignore.