Happiness arises from having meaning in life. There's the biologically derived meaning by creating a family. But it's not complete without personal and social "meanings". Working can provide both by overcoming challenges and by providing something useful to the nation. There's also the spiritual meaning  derived from "God". But refraining from making religious arguments. Without at least these 3 core sources of meaning, it becomes very hard or impossible to be fulfilled and then happy. Happiness comes and goes, but what really sustains it is the totality of meaning I referred to.

Money does buy all these products and services. It does affect the amount of worry or effort in a multitude of scenarios. However, money is ultimately a tool. A means to an end that, generally speaking, comes from work. Many of the scenarios you've raised can be obtained by other means of value exchange. The ability to be useful, possessing skills or making connections or being a good person, does provide many of the same, or even more, benefits that money can buy. Granted, many people can't have these traits. What, arguably, the vast majority of people have access to, however, is the ability to derive meaning from family, work, and contributing to society. With these 3 pillars, people can live very fulfilling and happy lives with no money. However, the reverse isn't true. Rich people who lack some or all of these 3 pillars are almost always never fulfilled and happy. There are plenty of examples to prove both of my claims. Either from the millions of families living happily in impoverished nations or from the rich kids, entrepreneurs, career people, etc., who are recurringly in varying degrees of misery despite their wealth. One of the best examples, I think, is the multiple cases of lottery winners going on a degenerate spending spree, losing all their money that could easily last a lifetime, and then reforming in some way and becoming happier.

I've argued that money does provide the ability to move in the world; it opens doors, prevents problems, and offers solutions. But it's a tool and a means to an end. It's reasonably demonstrated from psychology and philosophy, in the books like "Maps of Meaning" and from pattern recognition, that meaning is required for a fulfilling and happy life. Just as important as food and breathing. And that it derives from the 3 pillars that I've mentioned before. The other arguments and multiple examples that I have previously raised were to showcase that people can be happy without money and unhappy with money. It wasn't arguing for a rivalry or substitution or that money isn't important. It was to demonstrate that the most important requirement for a happy life is meaning. We can bring up examples of happy rich people, sad poor people, and how important money is for happiness. I would agree. But my point still stands. Meaning is the precursor core requirement regardless. From the sources I mentioned above, it can also be argued meaning is an instinct. For example, the "state of flow" that people reach by engaging in an activity that strikes the balance between knowing what to do and trying to solve a problem. Where people aren't overwhelmed by problems or being bored by knowing everything. Between chaos and order, this "state of flow" is often what's referred to as "required" in a job or work that's meaningful.