But I'm also a person who generally never experiences the issues some people have with Bluetooth in general. If I ever have an issue with Bluetooth on a computer, I swap out the wireless chipset with an actually good one. Its almost always just bad hardware. I've only had to do that a few times in the last decade though, more modern WiFi/BT chipsets are generally pretty OK. Its the old ones that are near worthless.
Although I will say most of the time I just plug in my USB authenticator. I normally only fall back to the QR code if I don't have my keys on me.
And as an edit, I wasn't aware fully that the QR code is to help assist the BT handshake, I had assumed it was posting a signed request back to the service. My bad, my above comment isn't completely correct. Thanks for cluing me in to the BT requirement for the QR code path.