Not sure if the OP had any resolution on this (I'm pretty sure I'm following their thread on the Corsair Help forum as well), but I'm having the exact same issue. I've tried the 'best reply' suggested answer using the USB 3.1 to USB-C/TB adapter (specifically the Apple one linked) and the behaviour is the same with both/either the receiver or the wired headset itself. I have checked my info vs. what y'all have added here seeing the same 500mA to 500mA for the receiver (headset itself reads as like 150mA out of the available 500mA with no other USB 3.1 items on the Mac when its just the headset itself plugged in, with the same blink in and out behaviour)
Attached youtube clip is from ~5min ago of attaching the wired Corsair HS80 headset to the Mac via the previously noted adapter in one of the Thunderbolt ports instead of the USB 3.1 ports https://youtu.be/eBdQCeuAxMk
If anyone is still interested in this issue or troubleshooting I can dig the million logs and screenshots I've sent to Corsair's help desk over the last 2 weeks if it would help.
I have a pair of SteelSeries Arctis 7 that have zero issues on this Mac Studio, but I hate the mic and fit quality vs. the Corsairs that have worked on both my PC and my Intel gen MacBook Pro I had from work previously.
To confirm and avoid any Bluetooth confusion this is specifically the HS80 Wireless headset, NOT the HS80 Max Bluetooth capable headset from Corsair.
