Bluetooth mouse disconnects and reconnects frequently on iMac 27-inch, Late 2013.

My spouse's 27-inch Late 2013 iMac seemingly randomly disconnects and reconnects the wireless mouse. Software is 10.15.7 (19H1615), Catalina.

Here is what I have tried to resolve the problem, non of which worked:

Tried with two different Magic Mouse, and two different Magic Mouse 2. All mice behave the same way on this computer, but behave normally on other computers.

Connected, disconnected, reconnected the mouse.

Reset NVRAM.

Deleted the Bluetooth preference list and HIToolbox.plist.

Safebooted.

Factory reset the mouse connection (Debug menu).

Reset the Bluetooth module.

The last thing I tried was ran Console and searched for bluetooth in the most recent system.log.

Looking at the entries when I think this was happening, I see these statements:

Jan 24 19:47:10 SuzanneneysiMac xpcproxy[3333]: libcoreservices: _dirhelper_userdir: 557: bootstrap_look_up returned (ipc/send) invalid destination port

Jan 24 19:47:15 SuzanneneysiMac AMPDevicesAgent[577]: Entered:_AMMuxedDeviceDisconnected, mux-device:43

Jan 24 19:47:15 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: Entered:_AMMuxedDeviceDisconnected, mux-device:43

Jan 24 19:47:15 SuzanneneysiMac AMPDevicesAgent[577]: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:43

Jan 24 19:47:15 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:43

Jan 24 19:47:15 SuzanneneysiMac AMPDevicesAgent[577]: tid:1f147 - Mux ID not found in mapping dictionary

Jan 24 19:47:15 SuzanneneysiMac AMPDevicesAgent[577]: tid:1f147 - Can't handle disconnect with invalid ecid

Jan 24 19:47:15 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: tid:ddb7 - Mux ID not found in mapping dictionary

Jan 24 19:47:15 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: tid:ddb7 - Can't handle disconnect with invalid ecid

Jan 24 19:47:31 SuzanneneysiMac com.apple.xpc.launchd[1] (com.apple.mdworker.shared.08000000-0600-0000-0000-000000000000[3314]): Service exited due to SIGKILL | sent by mds[136]

Jan 24 19:47:58 SuzanneneysiMac com.apple.xpc.launchd[1] (com.apple.mdworker.shared.0E000000-0000-0000-0000-000000000000[3307]): Service exited due to SIGKILL | sent by mds[136]

Jan 24 19:47:58 SuzanneneysiMac com.apple.xpc.launchd[1] (com.apple.mdworker.shared.0B000000-0300-0000-0000-000000000000[3347]): Service exited due to SIGKILL | sent by mds[136]

Jan 24 19:47:59 SuzanneneysiMac xpcproxy[3396]: libcoreservices: _dirhelper_userdir: 557: bootstrap_look_up returned (ipc/send) invalid destination port

Jan 24 19:48:05 SuzanneneysiMac AMPDevicesAgent[577]: Entered:_AMMuxedDeviceDisconnected, mux-device:44

Jan 24 19:48:05 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: Entered:_AMMuxedDeviceDisconnected, mux-device:44

Jan 24 19:48:05 SuzanneneysiMac AMPDevicesAgent[577]: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:44

Jan 24 19:48:05 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:44

Jan 24 19:48:05 SuzanneneysiMac AMPDevicesAgent[577]: tid:1f14b - Mux ID not found in mapping dictionary

Jan 24 19:48:05 SuzanneneysiMac AMPDevicesAgent[577]: tid:1f14b - Can't handle disconnect with invalid ecid

Jan 24 19:48:05 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: tid:1241b - Mux ID not found in mapping dictionary

Jan 24 19:48:05 SuzanneneysiMac AMPDeviceDiscoveryAgent[473]: tid:1241b - Can't handle disconnect with invalid ecid

Is there a clue as to why this is happening?

Is there a hardware failure?

Thank you for any suggestions.

Julian