>Isn't "movement in bed" how all sleep monitors work?
No.
The best ones monitor your brainwaves, and the best wearables monitor the next best ting, your hear rate and blood oxygen.
You can get knocked out by drugs, alcohol or just die in your sleep from apnea so you'll not move around in bed and your bed motion sensors are useless.
You need to tap into the body's vital signs to know your sleep stages accurately, especially REM.
For anyone interested in how Apple Watch measures sleep stages, here's a deep dive that goes into details about how the accelerator is used to estimate respiration rate, etc in order to classify sleep stages
I find wrist sleep apps accurate enough for showing me trends over time and correlations between things that make sleep worse (e.g. drinking before bed shows different sleeping patterns than not drinking). Interesting and useful data but I agree it's not scientifically precise.