Then you still have null, you’re just spelling it funny while confusing all the other developers who have to deal with your code and making it incompatible with language constructs like the nullish coalescing operator.
If the concept you are trying to express is “null”, then please use null to represent that instead of bringing in a poor substitute like an overloaded false.
For everything else, use false to “explicitly assign it”, you don’t need a third type.