macOS Full Bluetooth menu as default
There is no setting exposed directly to the user to make that change in the Bluetooth menu behavior, i.e. e.g., in System Preferences > Bluetooth > [] Show Bluetooth menu in menu bar, it only determines whether or not it's shown on the menu bar, not which menu is displayed by default or with modifier key(s) pressed upon being clicked. That is hard coded into /System/Library/CoreServices/Menu Extras/Bluetooth.menu.  Nor do I know of an indirect setting, e.g. using the defaults command, that can be used to achieve that which you've asked.

You'll just have to continue to option-click to get the secondary menu and shift-option-click to get the tertiary menu, or of course just click to get the default menu.