Your link claims any compound with carbon is organic (there are exceptions listed) which really doesn’t fit either since there so many exceptions.

I was glib with my organic chemistry because it’s not just hydrogen atoms specifically but more the covalent bond between carbon and hydrogen that makes it organic so they have to be bonded covalently to be considered organic.

There’s still exceptions to this definition but they’re far fewer and usually only found in extremely unstable compounds like the fully halogenated fringe cases you mentioned in another comment.