I have had the same problem across several Garmin Edge generations (model 1000, 1040, now again on 1050).
Using an iPhone, the text message feature never worked, even with all the Bluetooth channels enabled, and all the Smart Phone settings turned on.
I do get social media messages, and other app messages.
But I do NOT get a text message on Garmin Edge display from iMessages.
Running latest firmware 9.11 on 1050.
110% positive all settings and configurations are correct.
Went through 1st level tech support at Garmin. They had no answers.
Anyone else solve this issue?