GeorgeSoros The article linked by 23Sha-ger indicates that Garmin's emergency staff will be handling the messages, which will be carried by Skylo's geostationary system, which relies on a small tweaks to regular LTE.
Based on that information, there is no special tracking infrastructure. If the LTE modem is off, the phone can't talk to the satellite.
At this point it would be welcome if we could avoid repeated speculation about how maybe something unspecified about satellites could threaten something unspecified about privacy. If there is a plausible source affirmatively explaining a specific privacy threat, that would be of interest.
Meanwhile, regular cellular networks, by design, are tracking cellular users all the time. There are literally millions of cell sites, with sectorized antenna systems and beam forming, with legal requirements about localization accuracy.
The tracking threat (if it bothers you) is on top of the nearest apartment building, not in geosynch orbit. That system is tracking Pixel 9s, Pixel 8s, Pixel 7s, Pixel 6s, EOL Pixel 5s and 4s, Samsung phones, Fairphones, iPhones, etc.
To be clear, when there is an emergency, that tracking system saves lives. And when there isn't an emergency, that system delivers lots of bits per second to lots of devices.