Lunar can control the real backlight of the MacBook display by tapping into the private DisplayServices system framework.
The app only supports integer values between 0 and 100 but the framework supports floating point values between 0 and 1.
You can try installing Lunar’s CLI (https://lunar.fyi/#cli) and then running something like the following in a terminal:
lunar display-services SetBrightness builtin 0.005
That will try to set the backlight of the builtin display to 0.5%. Then you can try lower and lower values to see if they make any difference.
If you don’t see much difference between 1% and sub-1% values then there’s no way to dim the backlight further, and the only remaining method would be Gamma dimming which Lunar can do if you disable the Apple Native protocol from the Controls menu.