The APK is stored in the firmware system partition, and gets updated as a side-effect of OTA firmware updates. Thus, a certain OS version implies a particular APK version. The OS version numbers are more compact, so I'll use them to identify APK versions below.
v0.8.50 seems like a pre-prod version that accidentally got shipped on some early devices. Like all future versions, it sends the device's IMEI during account activation.
v0.8.67 is the "launch day" firmware. It sets the OS-Version and App-Version HTTP headers. It also sends the device's IMEI during authentication.