Sometimes the keyboard automatically pairs with one of the previously paired Bluetooth devices so it does not connect to new devices and shows a "connection rejected" error message on the newer computer. Please check if there are any other Bluetooth devices around your Keychron keyboard. If you do, you can try to:
(1) Remove other Bluetooth devices.
(2) Remove the keyboard from your Bluetooth list and restart the keyboard pairing again by holding fn+1/2/3 (fn1+Q/W/E for K6 and K12).