Razer Inc., my case finally got a sensible reply. Kudos, Romeo.
The issue is still not solved, of course. Yes, there seems to be no articles (at least official ones) that would confirm or deny Bluetooth support, but documentation does list "wearables", which can imply support for Bluetooth connectivity. The same article also links to doc about "HID LampArray", which is talking about wireless connectivity, but I am not sure if it means dongle-like connectivity or something more generic. Definitely something, that needs confirmation from developers.