Ended up getting this to work via USB Manager. Thanks Simon for the excellent plugin! Leaving all my notes here for future me or others:
Steps to use USB Manager to connect a remote Bluetooth USB dongle to a Home Assistant docker running on Unraid
Install usbipd-win on the remote Windows 11 PC host that we want to passthrough following instructions here ignore the parts about WSL.
Bind the device using
usbipd bind --busid=<BUSID>
Install USB Manager plugin on Unraid enabling HUB Processing, vhci_hcd, and Run USBIPD Daemon.
Install the NerdTools plugin to add BlueZ to Unraid host.
Add the remote host under the USB tab in Unraid and then Attach the shared device.
Check logs and determine driver being used? See my initial errors above.
Install the iwlwifi-cc-a0-77.ucode driver from Intel directly to /lib/firmware and rename the (original driver shown in logs) /lib/firmware/intel/ibt-20-1-3.sfi to /lib/firmware/intel/ibt-20-1-3.sfi.bak.
Attach the shared device again and should look something more like below.
Map the path /run/dbus container to /run/dbus as Read Only in my Home Assistant Docker. (no need to passthrough the actual device).
On restart of the HA docker, the device was automatically detected in the Devices & services menu. And it immediately detected the Airthings Radon BLE device that I started this adventure over.
This is what my logs showed when successfully connecting.
Jan 29 01:35:06 arcturus kernel: vhci_hcd vhci_hcd.0: pdev(0) rhport(0) sockfd(8)
Jan 29 01:35:06 arcturus kernel: vhci_hcd vhci_hcd.0: devid(65539) speed(2) speed_str(full-speed)
Jan 29 01:35:06 arcturus kernel: vhci_hcd vhci_hcd.0: Device attached
Jan 29 01:35:06 arcturus kernel: vhci_hcd: vhci_device speed not set
Jan 29 01:35:06 arcturus kernel: usb 5-1: new full-speed USB device number 23 using vhci_hcd
Jan 29 01:35:06 arcturus kernel: vhci_hcd: vhci_device speed not set
Jan 29 01:35:06 arcturus kernel: usb 5-1: SetAddress Request (23) to port 0
Jan 29 01:35:06 arcturus usb_manager: Info: rc.usb_manager usb_add 8087_0029 /dev/bus/usb/005/023 005 023
Jan 29 01:35:06 arcturus kernel: Bluetooth: MGMT ver 1.22
Jan 29 01:35:06 arcturus bluetoothd[64428]: Battery Provider Manager created
Jan 29 01:35:06 arcturus kernel: NET: Registered PF_ALG protocol family
Jan 29 01:35:07 arcturus usb_manager: Info: rc.usb_manager Add device with more than one interface & connect serial .
Jan 29 01:35:07 arcturus usb_manager: Info: rc.usb_manager Autoconnect Parent usb5
Jan 29 01:35:07 arcturus usb_manager: Info: rc.usb_manager Autoconnect No Mapping found 8087_0029 /dev/bus/usb/005/023 005 023 port 5-1
hciconfig seems to indicate that the device is seen, but I'm unsure where to go from here on troubleshooting.
hciconfig -a
hci0: Type: Primary Bus: USB
BD Address: 80:38:FB:E4:72:11 ACL MTU: 1021:4 SCO MTU: 96:6
UP RUNNING
RX bytes:1030 acl:0 sco:0 events:68 errors:0
TX bytes:2311 acl:0 sco:0 commands:68 errors:0
Features: 0xbf 0xfe 0x0f 0xfe 0xdb 0xff 0x7b 0x87
Packet type: DM1 DM3 DM5 DH1 DH3 DH5 HV1 HV2 HV3
Link policy: RSWITCH SNIFF
Link mode: PERIPHERAL ACCEPT
Name: 'BlueZ 5.71'
Class: 0x000000
Service Classes: Unspecified
Device Class: Miscellaneous,
HCI Version: 5.2 (0xb) Revision: 0x20f9
LMP Version: 5.2 (0xb) Subversion: 0x20f9
Manufacturer: Intel Corp. (2)