First I will say the culture series is one of favorite books. But I would start by suggesting a post scarcity society would be difficult in the limited size of our solar system. The main reason being resource theory. Like animals with unlimited food, they will grow in population untill there no longer excess food. Humans likely would do the same until there again is a limit of resources and things develop value. Ie. There is a limit of ocean front property thus we will make a reason to toil to better ourselves and get the best view.
But that diverges somewhat from the question you ask. Could we be happy in such a society if it could exsist? If we bring up the culture series, nearly every character in those books have purpose. Actually great purpose in that often they are doing some deed to better humanity. So it is hard to really use that as an example. So the question then becomes could a regular person be fully happy be having all their needs met and not having to do anything? I rather think of the hedonism bot in Futurama. He does nothing all day but all his needs are met. He has to expend zero energy. To me that seems quite depressing. I would rather be doing something to better myself and overall other people but in a post scarcity society there is nothing physically anyone would need thus there would be little I can contribute. Now could there be a true post scarcity society? I suggest not While money should not exsist, there will still be currency. That will be in the form of fame or talent or power. Creative people will be in demand and trade that for favors. Actors same in that they will gain favor. People in power will use their influence to have access to interests that others may not. But these people would be the minority. The majority of people always will be your average Joe. Will they be happy just comfortable exsisting? Honestly I really don’t know. Maybe we can evolve to that.
I will bring up one other point. In the history of humanity, during times of great difficulties are also the times when humans evolved the fastest. Could the opposite occur? If we have all our physical need met, might our overall intelligence decrease. I suspect it might. Then again, might it be better to be dumb and happy than intelligent and depressed?