I hope getting a location fix doesn't require actually sending anything to the satellite, as that would be a monumentally stupid design.

And then what? A.la. personal emergency beacons?

GPS Block IIIA actually does have a COSPAS SARSAT receiver on it and of course it can transmit on GPS frequencies. Today a Personal Locator Beacons doesn't think about the signals it receives from GPS other than as a source of location, but the intent is that a future COSPAS SARSAT upgrade will let the operators send a return message via GPS if they conclude you need rescuing.

Satellite based SMS would be pretty amazing for hikers/campers/etc.

This exists for at least a decade now.

AKA full-duplex

full-duplex transmission of data in two directions simultaneously in the same channel. SMS is a done via Beidou-1 satellites, and Beidou-1 don't serve as positioning at all today.

Beidou-2 is just like GPS, positioning service only, no SMS or shit.