I can’t stress enough that your own source says that a Kafka trap is when someone saying “I’m not X” is used as evidence that they are in fact X.

Here’s the definition again.

A Kafka trap is a fallacy where if someone denies being x it is taken as evidence that the person is x since someone who is x would deny being x.

Note the keyword if: this definition concerns a conditional statement. Affirming the conditional statement doesn’t require affirming the antecedent.

What if they are x? Conclusion trivially follows. If they aren’t, then they’ll deny. Neither possibility asserted? Doesn’t matter, because conditional statement is asserted: all possibilities lead to same conclusion. That’s the fallacy.

Consider the conditional statement: if the moon is made of cheese, then we can eat it. Is it true? Yes. Is the moon made of cheese? No.

(Re)learn logic.