Thanks for the detailed bug report. I did a bit of research on my side, apparently it's been broken for a long time,

Earlier report I can see is from 2021-09-02: https://bugzilla.kernel.org/show_bug.cgi?id=214287
Then in the Ubuntu bug tracker, 2022-04-11: https://bugs.launchpad.net/ubuntu/+source/linux-firmware/+bug/1968604

Looking at the linux-firmware Git repo, the pair of firmware rtl8761b and rtl8761bu were added in 2021-05-29, and then updated on 2021-11-25, as can be seen with:

<pre>
cd linux-firmware
gitk -- 'rtl_bt/rtl8761b*'
</pre>

I sent a message to the linux-bluetooth maliing list: https://www.spinics.net/lists/linux-bluetooth/msg103399.html

Thanks!!
This probably not the right place to ask.
And this question is outside of the report.
But can you tell me how does Linux/Kernel "know" which driver/filename to load?
Where is the lookup table (when you plug in a device) idVendor=0bda, idProduct=8771 in this case-
How does Linux get the information on what filename/driver to load?
I am going in circles with google searches trying to get an answer to this.

How does Linux get the information on what filename/driver to load?

It's really something in the kernel. This commit https://git.kernel.org/pub/scm/linux/kernel/git/torvalds/linux.git/commit/?id=9fd2e294. As you can see there, there's a mapping between firmware files, and the information that the kernel has about the device.

I'm no kernel specialist so I can't explain more in detail, sorry :)

This report has been filed against an old version of Kali. We will be closing this ticket due to inactivity.

Please could you see if you are able to replicate this issue with the latest version of Kali Linux (https://www.kali.org/get-kali/)?

If you are still facing the same problem, feel free to re-open the ticket. If you choose to do this, could you provide more information to the issue you are facing, and also give information about your setup?
For more information, please read: https://www.kali.org/docs/community/submitting-issues-kali-bug-tracker/