This can only happen if population is exploding or life expectancy is low. Neither is the case.

Increasing life expectancy is a population and economic problem, as it's expensive to keep people on past their ability to produce. Not that anyone is going to willingly give up their gains.

How do you plan to eliminate old people?

Often people don't appreciate grandparents until they pass away.

It's the opposite. Many/increasingly old and fewer young. With a strong anti-immigration and persistent anti-foreigner/xenophobic mindset.

How does immigration solve the issue. Once they become wealthier, their birth rate is going to drop, so you have to keep importing poor people from overseas to keep your GDP rising. Why not address the issue itself instead of trying to bandaid it.

Because Japan's population problem isn't a wealthy nation problem it's a population collapse problem. It's not just that birth rates have gone down because the average Japanese person has become wealthier or more educated. It's also that the lost decades made raising more kids unfeasible for a generation and because of that there's now a large elder population that must be taken care of by a smaler population. Immigration at least ameliorates some of that problem, plus the economy is doing better which means people will have more time and wealth to raise kids.

Even if you can't reverse the population decline you can at least not make it a dramatic collapse and go through all the human suffering that entails.

All developed countries have falling fertility rates, most below the replacement rate. Japan used to be the poster child for the issue, now they're not even the worst example. How many tens of millions of migrants would be needed to offset the unbalanced age pyramids in Japan, China, South Korea and all the Western countries beginning to experience the same problem? How could such a massive number of people integrate into a country?

The reason people don't have kids is not just the cost of doing so but the massive commitment it entails. People have more agency and mobility than they did before and they don't want to give that up. Importing people and ignoring that is printing more money to pay off current debts.

Now do the same narrative for Germany and Singapore and Korea who are on the same slope

And how would you solve the issue?

You have to let it happen. There will probably be a lot of suffering but rising labor costs will force solutions like automation. Most social issues in developed countries, like people having less and less relationships, are due to urbanization and technology which is more difficult to solve, but immigration is not going to fix that anyway. People recognize that endless growth is not sustainable but are too terrified of the alternative, as soon as it shows signs of slowing they want to keep it going by any means necessary.