Question: Can we be happy without being free?
Answer: You are completely right! We can’t be happy without being free.
The only question is: what do we need to be free from?!
True happiness is a positive collective emotional impression that arises from purposefully built, mutually supportive, mutually complementing Human connections.
And in order to build such connections, that are built on selfless, unconditional love and service of others, first we need to become free from our inherently self-serving, self-justifying, egoistic and hateful nature, which would never allow us to build such connections and become happy.