This is a personal POV, please read and build your own and discuss❤️
(My short answer: YES and NO)
What a beautiful question, though to be able to provide an answer, there is a need for proper understanding of what we're trying to define and what we're trying to answer and what better way is there other than a dictionary, that way we have an easier problem to work with.

Money: An asset used to facilitate exchange of value.

Buy: Acquire something of value in exchange for another thing of value, such as services or goods.

Happiness: emotions or feelings experienced when in a state of well-being.

Now logically, we can't get an abstract idea with a concrete object; So basically, No, Money does not buy Happiness, but, Happiness is a feeling that is produced after a set of enjoyment or satisfaction, and as humans we often experience that after acquiring certain assets or wins, and with money we can obtain them.
So technically money does actually buy happiness and its core value, hopefully my basic simple mind could solve this mystery.