Why does CHU-ZCT1 correctly pair with macOS, but CHU-ZCT2 fails?

I have 3 Dualshock 4 CHU-ZCT1 controllers

which perfectly pair via Bluetooth on

a 2008 Macbook running OS X Mountain Lion and

a 2015 Macbook Pro running macOS Sierra and later High Sierra.

.

I have 1 Dualshock 4 CHU-ZCT2 controller

which fails to pair via Bluetooth on

a 2008 Macbook running OS X Mountain Lion and

a 2015 Macbook Pro running macOS Sierra and later High Sierra.

.

I have tested other Dualshock 4 CHU-ZCT2 controllers

which also failed to pair via Bluetooth to the aforementioned devices.

.

.

(All controllers connected without issue to a PS4 device.)

.

.

Why did the firmware update break macOS functionality?