An American English Usage Question From a Native Speaker of That Tongue

Allow me, for the moment, to forgo to the traditional groveling about my failure to post- there is little excuse.

Rather, I have a question about standard American English usages of contractions with the verb "to have".

I'm going to provide a number of sentences that would sound weird to me, and then rewrite them to what sounds "normal" for American English usage as I understand it. Please tell me if I am full of shit and the original phrasing sounds perfectly normal American English to you.

CONFUSING: I haven't any money.

REWRITE: I didn't have any money.

***
CONFUSING: I haven't any money.

REWRITE: I don't have any money.


But things like, "I haven't had breakfast," where "haven't" serves as a "helping verb" sounds perfectly fine to me.

Am I out of my mind on this? Is this just a part of normal US English that I have totally not stumbled upon before? Or does this sound weird?