I think the problem with your proposal is that its entire rationale is simply “The eq method and ‘==’ operator has a corresponding ne method and '!='operator. Ergo, to maintain consistency, there should be a dunder method and operator that acts as the inverse of the bool method.”.
In general, consistency in the design of a a programming language will usually but NOT always enable it to have more use cases.
If a maintainable inconsistency in the design of a programming language will have more use cases than trying to make them consistent, then what utility is there to proceed with the latter option?
Consider PEP 207 which allowed for the independently overloading of the dunder methods associated with the <, >, <=, >=, ==, != operators and how that allowed for operations that were before considered to be opposite and symmetric to have asymmetric implementations. There were use cases for that inconsistency (check the PEP itself) and as such it was implemented.
For a more recent example, consider how PEP 635 specifies that the str, bytes, and bytearray classes shouldn’t have their instances be pattern matched with cases that are looking for sequence patterns, despite them being also being Sequence subclasses. The use cases of those classes as ‘atomic’ types were so widespread that users were confused when the instances of those classes were matched and as such that inconsistency was developed.
Consistency isn’t a hard rule to be adhered to and corrected for at all times. It’s first and foremost a DESIGN GUIDELINE, and a motivation to implement a new feature second.
So if you want this feature in Python, specify use cases that are worthy enough to warrant the implementation of your feature. As right now, you haven’t provided any use cases that would warrant the implementation of a not bool method and operator.
(The below section was written before the typing tag was removed)
Also please get rid of the typing tag you marked on this post. It’s could be very misleading for other users as the subject matter doesn’t involve type checking whatsoever. Other users have already pointed it out and may continue to do so. Failure to remove the tag could convince them that you are willing to not only clickbait them but also act in bad faith, thereby discouraging users to consider and engage with your post. I’m not saying you are acting in bad faith right now, just that it may come off that way if you don’t correct for it.