Having this same issue myself.  All I wanted was to purchase another one.  But no, they told me they don’t sell them separately.  My headset is still under warranty but they are denying that because I can’t locate the original email from my purchase, as if that negates the fact that I have a 200$ headset that I can’t use for its intended purpose because I broke the dongle.  Save yourself the stress and purchase somewhere else next time.

I’m usually a quiet person. But I’m quite frustrated, long story short I also have a broken dongle, and did all the same searching and ended up with the same result. no help. I’ve had my headset long enough that I wore the serial number right off the sticker on the left cup. a quality product is why i bought it, having faith in a company that's supposedly “for gamers, by gamers” maybe they should think about their motto, since most of us save for upgrades, not replacing working peripherals. Reminds me of Apple painted black, Anyways heres a link to another thread where someone did get help. 

"https://insider.razer.com/razer-support-45/why-there-is-no-razer-kraken-v3-pro-usb-wireless-transceiver-in-replacement-parts-53706?tid=53706&fid=45"

offer the dongle on your store, offer a method of making other dongles compatible, or preferably stop occupying usb ports and use Bluetooth. I look forward to hearing about a solution since the headsets are still on amazon.