The 7 Mbit/s are for an entire cell, i.e. all devices simultaneously transmitting in it, not per device.
Iridium (a comparable system) used to support about 10 Mbit/s per satellite in its first satellite generation, which had 48 spot beams each. The second generation supports about a megabit per modem, but these have larger antennas than a regular satphone.
> Apple doesn't disclose the bitrate of their Emergency SOS feature but it uses Globalstar's L-Band for uplink and I believe the bitrate of that channel is 9.6 kbps.
I'm almost certain Apple doesn't even use the full 9.6 kbit/s modulation scheme for their emergency SOS feature: As you mention, it's way too slow for that (having used it myself – even just transmitting my location takes a couple of seconds, and that's a message of only a few bytes).
Globalstar satellites are bent-pipe relays, so Apple could be using whatever custom modulation and coding scheme they need to stay within the constraints of their power and SNR envelope. With the iPhone's built-in antenna and transmit power (around 2 watts or so, if I remember correctly), I'd be surprised if it was more than a couple hundred bits per second.
Regular (i.e. non-smartphone) satellite messengers are much faster than that and only take a few seconds to transmit and receive messages of hundreds of bytes.