Apple Mouse and keyboard connectivity with 10.15.6

The following will require any USB keyboard an mouse. If you don’t have them, borrow or buy them, they are inexpensive!

1.     Connect the USB keyboard and mouse to the computer.

2.     Open System Preferences – Bluetooth

3.     Un-pair the wireless keyboard and mouse.

4.     Turn off Bluetooth

5.     Restart the computer in Safe Mode per the directions in https://support.apple.com/en-us/HT201262

6.     Restart the computer normally.

7.     Open System Preferences – Bluetooth

8.     Turn on Bluetooth

9.     Re-Pair the wireless keyboard and mouse.

10.  Unplug the USB keyboard and mouse and begin testing the wireless devices again. 

Then please do the following:

Please navigate to the Mac App Store and download the free version of EtreCheck OR please click www.EtreCheck.com where you will find the app. Once you have downloaded the free app and created the report please post it as your reply to this message. In order to post it, please use the following link for more detailed instructions on how to correctly include the results: 

https://discussions.apple.com/docs/DOC-250000211

We can then look for obvious issues that may be causing your problem.

None of the usual suspects, I would for the detailed instructions again in my initial post. Also try resetting the NVRAM and restarting in Safe Mode.

NVRAM Reset & Safe Mode Reset instructions

Do you have any third party antivirus, security, cleaning or any other type of third party "maintenance" apps installed?