Departing from the country

Is the prohibition against leaving the country generally still valid today? After all, the country has been pretty empty of Jews for the past two thousand years, and even today, when there is a Jewish state in Palestine, there are millions of religious and ultra-Orthodox Jews who remain to live abroad, and some even claim that there is a prohibition against living in the Land of Israel before the coming of the Messiah. Does it make sense to say that they are acting contrary to the halakhic law?
I saw on Wikipedia the halakhic entry in question that when there is a danger to living in Israel, one must fight for it even to the point of giving up one's life. Doesn't this contradict the permission to leave it when there is a basis for assuming that it is in danger?
Many thanks

Absolutely yes. Poskim have already written that there is a difference between not immigrating and leaving the land. Similarly, Maimonides’s bearers of arms wrote in Halacha Melchim about returning to Egypt (he himself lived in Egypt).
Does the fact that many people do something qualify him? There are also many who speak slander. It is true that here some of those many also think that it is permissible (in the sense of slander), and yet. Furthermore, how do they think that there is a prohibition in this if many people do it? There is no similar argument against them?
The commandment to conquer the land, unlike Yeshiva Haret, is imposed on the public. Today, the Jewish public is different and in my opinion there is no commandment to conquer the land. Therefore, all our wars today do not fall within the scope of conquering the land but rather helping Israel from a difficult situation (i.e., protecting life). One of the implications (which I discussed in column 609) is the obligation of Jews from abroad to join.

Is there a case for permitting immigration and settlement in another country even in cases where a person does not believe that the State of Israel is in existential danger, but living there causes him mental distress due to other reasons, such as a general fear of difficult security situations (which do not necessarily include an existential danger to the state), a poor economic situation, a feeling of social alienation, etc.?

It's hard to give sharp definitions here. There is permission to leave the country for livelihood purposes and to stave off hunger, and it seems to me that mental distress is no worse than these.

But isn't the permission to leave the country for the purposes of earning a living and breaking hunger only for the purpose of temporary departure? I'm talking about immigration and settlement.

This is also temporary. When the situation improves, it will return.

But is he allowed to leave in the first place with the intention of settling, when he does not believe that in the future he will return to settle in Israel again?

It doesn't matter what he believes. It matters what he does and why.