Money will _absolutely_ buy happiness. Whoever tells you otherwise is fooling you.
Yet there seem to be many other things playing a role in happiness. Besides the famous ones like love, I can cite Ikegai, Wanderlust, Ubuntu, Hygge, Wabi-Sabi (...), and it may be foolish to concentrate on just one of them.
Money can alleviate hardship and stress, but happiness is more than absence of sadness, hardship, or stress.
Indeed: happiness seems to require a certain degree of introspection to realize other things, such as social status or Ikegai, are needed too - hence the (also) famous corollary "Ain't got enough money to pay me respect; Ain't no budget when I'm on the set; If I like it, then that's what I get, yeah"
My favorite philosopher indeed!
Other than mental health issues, 99% of the problems that might cause unhappiness can be solved with money (though money not be the only factor).
Problem: Your mother requires an expensive medical treatment to prevent her from dying.
Solution: $$$
Your mother being dead may cause sadness, but that's not from a problem because there is no solution to someone being dead. That type of sadness is a normal, human emotion. It's entirely different to feel sad because of unchangeable realities than because you don't have enough money to fix the thing that's making you sad.
Enough money can buy the health (up to a point) of yourself, your family, your friends, and even your acquaintances. It can give you the breathing room to develop meaningful connections, to go to therapy, to exercise.
You might not be happy with money, but it has the potential to solve all the problems that affect you directly, and affect everyone you know directly.