I recently had an unrepairable puncture in one of my MY2021 Outback's tyres, and was surprised to see it kept reading the pressure of the faulty tyre in the boot after I'd swapped it, and eventually the whole system shut down with a TPMS error.
I now know:
[1] The sensors are not purely powered by movement, they contain a lithium battery rated for 7 years life.
[2] The factory spare wheel does have a sensor,but it has not been "activated". It won't work until this has been done. Your dealer can do it during a service, or most tyre shops should have a programming tool to do it (they're about $350 on eBay) (edit. see next post!)
[3] Once all five wheels are "activated", the car should auto detect which sensor is on which corner of the car (and ignore the spare in the boot) (Edit: MY2023 onwards)