Comment 43 for bug 1738838

Same problem:

MPOW Bluetooth 5 dongle (Model: BH456A)

$ uname -a
Linux dg-dl 5.8.0-44-generic #50~20.04.1-Ubuntu SMP Wed Feb 10 21:07:30 UTC 2021 x86_64 x86_64 x86_64 GNU/Linux

$ rfkill
ID TYPE DEVICE SOFT HARD
 1 wlan phy0 unblocked unblocked
 6 bluetooth hci0 unblocked unblocked

$ lspci
00:00.0 Host bridge: Intel Corporation 4th Gen Core Processor DRAM Controller (rev 06)
00:01.0 PCI bridge: Intel Corporation Xeon E3-1200 v3/4th Gen Core Processor PCI Express x16 Controller (rev 06)
00:14.0 USB controller: Intel Corporation 8 Series/C220 Series Chipset Family USB xHCI (rev 05)
00:19.0 Ethernet controller: Intel Corporation Ethernet Connection I217-LM (rev 05)
00:1a.0 USB controller: Intel Corporation 8 Series/C220 Series Chipset Family USB EHCI #2 (rev 05)
00:1b.0 Audio device: Intel Corporation 8 Series/C220 Series Chipset High Definition Audio Controller (rev 05)
00:1c.0 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #1 (rev d5)
00:1c.1 PCI bridge: Intel Corporation 8 Series/C220 Series Chipset Family PCI Express Root Port #2 (rev d5)
00:1d.0 USB controller: Intel Corporation 8 Series/C220 Series Chipset Family USB EHCI #1 (rev 05)
00:1f.0 ISA bridge: Intel Corporation C226 Series Chipset Family Server Advanced SKU LPC Controller (rev 05)
00:1f.2 RAID bus controller: Intel Corporation SATA Controller [RAID mode] (rev 05)
00:1f.3 SMBus: Intel Corporation 8 Series/C220 Series Chipset Family SMBus Controller (rev 05)
01:00.0 VGA compatible controller: NVIDIA Corporation GM107GL [Quadro K1200] (rev a2)
01:00.1 Audio device: NVIDIA Corporation GM107 High Definition Audio Controller [GeForce 940MX] (rev a1)
03:00.0 PCI bridge: ASMedia Technology Inc. Device 1182
04:03.0 PCI bridge: ASMedia Technology Inc. Device 1182
04:07.0 PCI bridge: ASMedia Technology Inc. Device 1182
05:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 15)
06:00.0 Ethernet controller: Realtek Semiconductor Co., Ltd. RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller (rev 15)

$ dmesg | grep -i blue
[ 2.641328] usb 3-7: Product: Bluetooth Radio
[ 6.626592] Bluetooth: Core ver 2.22
[ 6.626603] Bluetooth: HCI device and connection manager initialized
[ 6.626606] Bluetooth: HCI socket layer initialized
[ 6.626607] Bluetooth: L2CAP socket layer initialized
[ 6.626608] Bluetooth: SCO socket layer initialized
[ 6.860576] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 6.861534] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 6.861534] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 6.903755] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 6.903759] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found
[ 97.431707] Bluetooth: BNEP (Ethernet Emulation) ver 1.3
[ 97.431708] Bluetooth: BNEP filters: protocol multicast
[ 97.431711] Bluetooth: BNEP socket layer initialized
[ 246.400802] usb 3-8: Product: Bluetooth Radio
[ 246.406937] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 246.407880] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 246.407884] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 246.407925] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 246.407929] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found
[ 268.373795] usb 3-6: Product: Bluetooth Radio
[ 268.377141] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 268.377947] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 268.377952] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 268.378019] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 268.378025] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found
[ 330.775006] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 330.776000] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 330.776003] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 330.776037] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 330.776040] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found
[ 418.646117] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 418.647121] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 418.647125] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 418.647168] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 418.647172] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found
[ 435.976571] usb 3-7: Product: Bluetooth Radio
[ 435.980209] Bluetooth: hci0: RTL: examining hci_ver=0a hci_rev=000b lmp_ver=0a lmp_subver=8761
[ 435.981140] Bluetooth: hci0: RTL: rom_version status=0 version=1
[ 435.981143] Bluetooth: hci0: RTL: loading rtl_bt/rtl8761b_fw.bin
[ 435.981169] bluetooth hci0: Direct firmware load for rtl_bt/rtl8761b_fw.bin failed with error -2
[ 435.981171] Bluetooth: hci0: RTL: firmware file rtl_bt/rtl8761b_fw.bin not found

Turn on switch in settings/Bluetooth - icon remains grayed out "Bluetooth Turned Off"

Reboot doesn't help.
Shutdown, remove power, restart doesn't help
Pull BT USB interface, reinstall/change port, doesn't help

The following procedure worked for me:

https://www.xmpow.com/pages/download
https://mpow.s3-us-west-1.amazonaws.com/20201202_mpow_BH456A_driver+for+Linux.7z

expand and cd into /20201202_LINUX_BT_DRIVER/rtkbt-firmware/lib/firmware

$ sudo cp rtl8761bu_fw /lib/firmware/rtl_bt/rtl8761b_fw.bin
$ sudo cp rtl8761bu_config /lib/firmware/rtl_bt/rtl8761b_config.bin
$ sudo rmmod btusb
$ sleep 1
$ sudo modprobe btusb

Following this, I was able to turn on BT and pair with devices.