There are many approaches for a business to be both good and also make profit

That’s literally not possible. Making profit means that a business is robbing the rest of society, including its workers.
The presence of the profit motive in an economy has a bunch of other consequences, including things, like the lack of guaranteed housing, which is also ghoulish.

Just as an example, in the periods of comfort, they can focus only on profit. However, in the times of crisis, businesses can instead focus on doing social good

That’s literally not possible. The owners of a business are systemically only interested in a business so long as it provides them with net wealth over their investments, which requires a business to be profitable.
There is no systemic interest for these owners to literally do something antithetical to maintaining their businesses and sacrifice profits for the common good. The only reason for them to do that would be if they were forced to. However, that would require another sufficiently powerful party to be interested in doing so.

but thing is many small businesses around the world

Small businesses also have additional issues that prevent them from actually being net good for society, like the fact that they are less efficient and less technologically innovative.

I am really sorry if you don’t enjoy exams, because I also hate exams.

I do not hate exams. Exams are necessary.
The question is, what humanities and/or art disciplines would you force somebody who chose a STEM specialisation to take exams in to be allowed to graduate, and why?

first I just want to focus on the question what is the purpose of education.

The purpose of education from the standpoint of a state or another sort of group is to reliably produce people capable of some specialised labour (and - usually - to instill them with a worldview that would make them more loyal to said group). Considering that it is states that organise serious education, that’s the only ‘purpose’ that matters.
I hope we are not going to conflate ‘purpose of smth’ with ‘reasons to appreciate smth’. I appreciate education quite a bit, and study almost every day.

I strongly believe that the education helps us to be a better human being

I apologise, but this is rather wishy-washy.
What does ‘a better human being’ even mean? Why would that be in any way important for the people that you decide to force this opportunity to fail to graduate? Why would that be important for a given group that organises a given education effort? Why would that be important to the rest of a relevant society?

Despite the ‘STEMlord’ stereotype of engineers, software developers, and people who do the ‘hard’ science-related stuff being horrible people, I do not think that humanities and art specialists are better. There is a lot of extremely heinous stuff that they say and that gets promoted a lot, including in education. So, I would not really say that humanities would help make a person ‘better’ in any sense that I would recognise as such.

beyond just being a better doctor or a better software developer or a better engineer.

Well, what I wanted from education is to be a better software developer and mathematician. So, if we are to consider my case, I neither wanted nor needed to be better at recognising that most people have no understanding of what idealism is, for example, and to have my degree hinge on taking a philosophy exam where the teacher couldn’t even give any workable definitions. That stuff is completely useless for me in both my personal life, and my professional activities, and has also contributed to me being less able to fit in - including on these very forums, - I would argue.

So, as it happens, the oppressors might establish a monopoly over the fresh water that reaches the village due to aforementioned project. So, despite the project providing some benefit, to the oppressors, it provides almost no benefit to the oppressed class. No engineer would consider these kinds of societal issues while designing the project, despite knowing about the casteism and understanding it’s consequences because they are not educated to combine their engineering skills and know-how with the casteism.

I don’t see how a humanities education would help here, especially in the case of low-level junior engineers (as opposed to senior and leading engineers). What actionable insight could be provided, by what humanities discipline(s), and how much of an engineering curriculum should be sacrificed for teaching those skills? Most importantly, why would engineers opt to use this insight for common good even if they reach it?
From what I can see, if the humanities courses are short, the engineers will not get much in terms of reliable knowledge that isn’t already covered through cultural osmosis. If the courses are long, it means that they get taught significantly less about engineering.

These projects should not just have economic utility, but also social utility or at least should not have negative social utility.

Okay, but that’s not for a low-level engineer or developer to make any relevant decisions about, and a humanities education doesn’t mean that a person would be any more inclined to implement the solutions that have more social utility.

Consider the impact of plastics, fossil fuel and their pollution on the society and individuals. However, for decades, we gladly kept building new roads to accommodate more vehicles purchased by rich people, despite knowing about them.

Okay, but how would a more humanities-focused education of engineers/scientists/etc. improve things in this case? Do you have any evidence for relevant claims?

My hope is that with a humanities education, it will make more engineers to evaluate the social utility of their projects and not just the economic utility.

What would force or make them more inclined to evaluate the social utility in these cases? And what about the engineers/developers/etc. who do not get to make any relevant decisions? And how would humanities disciplines help in making these evaluations?
Also, it doesn’t actually require one to be educated in things like ‘is this ethics system an emotivist one?’ and ‘which of these legal documents has a higher priority?’ in order to want to improve people’s lives, nor does being educated in them make a person not a ghoul.

Considering that humanities specialists - just like STEM specialists - are usually either horrible judges of social utility, or are just outright ghoulish, I don’t really see why one would think that humanities disciplines would change anything relevant.

One interesting theory that I came across was in a book called “Development As Freedom” by Amartya Sen, a Noble Prize winning economist. In the book, he puts forward the idea that “Economic Development must increase the freedoms of individuals and society”. In essence, contrary to popular measures of economic development like GDP, Per Capita Income, he straight-up wants to quantify (or at least qualitatively) the impact of economic and market activity through their social utility.

Is it an actual theory, or just some platitudes about wanting to study those things? Because if it’s the latter, then I fail to see the novelty, as many people have studied relevant things before him.

In essence, all human activity has the goal to serve the humans (both individual and society), this world and the nature we live in.

That is quite obviously not true. People very obviously do, in fact, do things with selfish goals. For example, business owners implementing solutions to profit at the expense of the rest of society, or NATO leaders maintaining a brutal colonial hold over the world.
No amount of humanities education is going to change what a person’s social and economical interests will be, which are the primary factors in people’s behaviour on a systemic level, I would argue.