I hadehad the same issue where I could not find Change Keyboard Type in that interface after migrating to new Mac with Big Sur. Not a hardware failure and wanted to force keyboard re-identification.
Deleting /Library/Preferences/com.apple.keyboardtype.plist
(as suggested above by JMY1000) and rebooting solved it. After the reboot the system ran the keyboard setup again and I could set the correct type.