Sperm donation

Does the Rabbi think that there is no value in bringing children through donation? And is this just a psychological/egoistic need of the parents?

Define my intention more..
Is it in our generation when there is a possibility of having children even for an infertile couple through donation
And in fact even with in vitro fertilization there is no fulfillment of the mitzvah of Pro and Ro?
Maybe there is value in having children through donation.. Is this also the existence of the world?

There may be some value in this, but it is negligible compared to the problems. In general, today having children is questionable in how much value it has (population explosion) except for the mitzvah (therefore, the mitzvah of Shabbat is now null and void. There is no fear that the world will be in chaos if we are not clean of Shabbat). And when you are exempt from the mitzvah, there is certainly no reason to get into trouble for it.

The value in having children is not only to escape the fear of chaos, but also to include the image (meaning the abundance of the image of God in the world), and beyond that, there is a connection here with the child himself, for although it is said that it is not convenient for him to be created, it is nevertheless probably good for him to be created (“good” is different from ”comfortable”) because it is reasonable to assume that if God created man, He probably did so, among other things, for the benefit of man.
Beyond that, there is the fact that it is probably about that child being raised according to Torah and mitzvot, and here there is value at all, since the number of observant Jews in the world is not that large. In addition, a person who is raised according to Torah and mitzvot is usually a person who contributes to society above average. In fact, almost every person born in Western society today creates a positive effect on the world. After all, the expected contribution to the GNP is expected to generate a lot of tax revenue that will usually be transferred to positive purposes for society, such as education, health, science, etc.
Perhaps we can also add here the issue of settling the Land of Israel, and strengthening the Jewish people's hold on their land.

As far as I remember, the halakha is about Shabbat Yatzra. There is no obligation to breed with a creature that is not in the world, and there is also no obligation to make him perform the mitzvot.
As for the question of whether a child in Western society makes a positive contribution to the world, I am really not sure.
Regarding strengthening the nation and its hold on the land, here I am very hesitant. This is an argument that comes up a lot, but on the other hand, every nation and every group is sure that they are unique and therefore it is important for them to reproduce. Only the others should refrain. According to the categorical imperative, the rules of morality should be universal, so I am not inclined to accept this argument. Of course, things would be different if we had a real problem of holding on to the land (in the sense of a dead person being laid before us). But as a general statement, it does not seem so to me.

Even if the Chinese or Indians think they are unique, I don't think they think it's important for them to reproduce. Partly because they feel safe enough in terms of demographic threats. On the contrary, the Chinese have even limited their own birthrate despite all that they think they are special. The Jewish people are in a situation where they are fighting for their right to their land, a relatively unique situation that most people are not in, most people are safely sitting in their land with nothing to fear. Not only that, but the enemies of the Jewish people outnumber them tenfold (when you take into account the entire Arab world).
Beyond that, the multiplicity of God's image in the world is a consideration that applies to all nations.
In addition, from an economic perspective, the more people there are in the world, the more efficient humanity will be. This stems from the fact that the "overhead costs" will be distributed over more people. There may be reservations about third world countries where high birth rates can be a burden on the global economy, but in developed countries, I think that high birth rates are an economic blessing. It is not for nothing that one of the indicators of the economic strength and stability of a developed country is a "healthy" birth rate (although not an excessive one). As soon as a country's birth rate falls below 2.1, the aging population becomes a large proportion of the productive population, and then they become a burden that is already difficult to bear. The falling birth rates in the Western world have recently led to the creation of policies encouraging birth rates by various governments.

In my opinion, a person in the first world is much more of a burden than a person in the third world (who is close to starving and does not harm the climate and conditions here in any way, and does not produce garbage and pollution). What is lacking today is not money but the desire to give it and help. Donating to world money is not really important here. I do not think that the consideration is financial (therefore, overhead costs are not important either). What is lacking (or is about to be lacking) is space and natural resources, not money. Money is not a resource but a form that society has developed to distribute resources within it.
Appropriate birth rates are indeed mandatory even today. But this is so that the young can maintain the elderly in society (the inverted age pyramid that China suffers from and therefore changed their policy, as you yourself mentioned). I did not talk about falling below it but about considering it. From the point of view of halacha, there is no consideration for this and the more, the better.
As mentioned, if we really are in a situation where we need more for security reasons, etc., I also agree. What I argued is that general statements are not enough.

Besides the commandment to Shabbat Yatzra, there are a few additional things:
Rambam, Laws of Wives, Chapter 15
Even though a person fulfills the commandments of fertility and multiplication, he is commanded by the words of the scribes not to refrain from fertility and multiplication as long as he has the strength, for whoever adds one soul in Israel is as if he had built a world.

According to the Rambam, the reason why it is necessary to add fertility beyond this minimum is from the fundamental value of the creation of man. Just as there is value in avoiding murder and this is a postulate, the value of the creation of man can be seen as a postulate (postulate = no further reasoning is required). Chazal also linked bloodshed to the avoidance of fertility, and so he brought in the Shulchan A in Even HaEzer Laws of Feriy and Multiplication, Section 1: Every man is obligated to marry a wife in order to multiply and multiply. And anyone who does not engage in fertility and reproduction is like shedding blood, diminishing the image, and causing the Divine Presence to depart from Israel.

In addition, I saw a reference by Rashi to the matter that brings evidence from the verse to "In the evening do not let your hand rest":
Rashi, Tractate Bitzah, page 37, page 1
"He shall have a wife and sons" - two males for the house of Shammai, or a male and a female for the house of Hillel, and nothing else is specified in the whole land, as we say in Yevamot (66:2), and from what, a little commandment is given here, as it says in Yevamot (66:2), and from what, a little commandment is given here, as it says in the morning sow your seed and in the evening do not let your hand rest" (Ecclesiastes 11).

And something like this in Yevamot, page 32, page 2
Rabbi Yehoshua says: A man takes a wife in his youth - he takes a wife in his old age, he has sons in his youth - He will have children in his old age, as he said: In the morning sow your seed and in the evening do not withhold your hand, for you do not know whether this will prosper, or whether both of them will be good.

Rashi D. Will this prosper? Which seed will be righteous and fear God and will endure.

That is, beyond the matter of settling the world and preventing it from returning to chaos, there is also value in bringing righteous and fearing people into the world. And this is certainly more likely to come from people who are Torah-observant and mitzvot who educate in Torah and fear of God.

Indeed. But these are all reasons given by Rishonim or hints as a reason for reading. The law itself is for the Sabbath to be created. To the best of my judgment, these reasons do not stand up to the considerations I presented.