Continuous Bluetooth timeouts [Broadcom BCM20702A]

My computer is an ASUS A88XM-A with AMD A8-7600 Radeon R7. Pluggable USB 2 Bluetooth dongle. Logitech K480 Bluetooth keyboard and Keychron K7 Bluetooth "keyboard".

The Bluetooth manager finds the K480 but pairing always fails. The keyboard flashes blue but dongle steady blue.

The K7 does not even show up. (But then the "keyboard" does not even work using a USB cable.)

Bought dongle and K480 4 years ago, never got them to work at all, gave up as a bad investment.

I ordered a K7 wireless keyboard. What I received was a Bluetooth keyboard. Bluetooth does not work. Plugging it in with a USB cable partially works (function keys and End key do not work).

Got the K480 working with my Samsung Galaxy 5 Android tablet, but not with my computer. I want Bluetooth but do not know how to get it to work. It still does not work after 4 years of cold boots and the replacement of the power supply.

I went to the Keychron Facebook Linux group. They were complaining that Ubuntu does not support Bluetooth and that the Keychron function keys do not work.

ProblemType: Bug
DistroRelease: Ubuntu 20.04
Package: bluetooth (not installed)
ProcVersionSignature: Ubuntu 5.13.0-35.40~20.04.1-generic 5.13.19
Uname: Linux 5.13.0-35-generic x86_64
ApportVersion: 2.20.11-0ubuntu27.23
Architecture: amd64
CasperMD5CheckResult: skip
CurrentDesktop: MATE
Date: Wed Apr 20 10:45:57 2022
InstallationDate: Installed on 2022-03-05 (46 days ago)
InstallationMedia: Ubuntu-MATE 20.04.3 LTS "Focal Fossa" - Release amd64 (20210819.1)
InterestingModules: rfcomm bnep btusb bluetooth
MachineType: System manufacturer System Product Name
ProcKernelCmdLine: BOOT_IMAGE=/boot/vmlinuz-5.13.0-35-generic root=UUID=0fc4c88c-4da7-4b59-afcc-1de5d036e6ba ro quiet splash
SourcePackage: bluez
UpgradeStatus: No upgrade log present (probably fresh install)
dmi.bios.date: 04/01/2014
dmi.bios.release: 4.6
dmi.bios.vendor: American Megatrends Inc.
dmi.bios.version: 1301
dmi.board.asset.tag: To be filled by O.E.M.
dmi.board.name: A88XM-A
dmi.board.vendor: ASUSTeK COMPUTER INC.
dmi.board.version: Rev X.0x
dmi.chassis.asset.tag: Asset-1234567890
dmi.chassis.type: 3
dmi.chassis.vendor: Chassis Manufacture
dmi.chassis.version: Chassis Version
dmi.modalias: dmi:bvnAmericanMegatrendsInc.:bvr1301:bd04/01/2014:br4.6:svnSystemmanufacturer:pnSystemProductName:pvrSystemVersion:rvnASUSTeKCOMPUTERINC.:rnA88XM-A:rvrRevX.0x:cvnChassisManufacture:ct3:cvrChassisVersion:skuSKU:
dmi.product.family: To be filled by O.E.M.
dmi.product.name: System Product Name
dmi.product.sku: SKU
dmi.product.version: System Version
dmi.sys.vendor: System manufacturer
hciconfig:

rfkill:
 0: phy0: Wireless LAN
  Soft blocked: no
  Hard blocked: no