First, real estate is almost always inherited, not purchased over the course of your life (it's far too expensive relative to anything but the top few % of incomes, and mortgages are somewhat hard to get). Also, overall economics are family-level not individual-level. Often only one or two people in the extended family has a job, and the money goes to the entire family.
Second, families growing at more than replacement result in the ancestral land being divided into smaller and smaller lots. The deed ('red book') tends to be inherited by the eldest son (but not as often as you'd think), but the actual space allocated (by a contract separate to the deed) tends to depend on direct-family size.
So there's this weird dynamic right now, where having kids early, and relying on extended family to support them lets you seize more of the family real estate. Inheriting more of that is worth more than any accumulated salary you could earn due to skyrocketing prices. So from what I gather from the rumor mill, there's some scheming to have more kids earlier than your siblings, and pressure older family members to allocate you more property -- instead of working or building a career. So the motivation to have children is very different here than in Japan!
In part because of these things, I think 3 or 4 people on my street have what you would typically call a full-time job. Most live 4 to a small room rent-free, and stay home all day. I estimate within 10 or 15 years many will be priced out of their homes, which will be demolished to make room for large complexes of tiny rental rooms that the infrastructure will really struggle to support. A few big units are already being built in the area ever year.
So if countries like Japan want to attract immigration from here, we've got a generation just being born that would probably be willing to consider long-term opportunities in Japan. It is already quite popular to go to Japan or Korea to work menial jobs under the guise of 'studying' for a couple of years. Some education is often provided, but it's mainly paid job placement at varying levels of shadiness. If that can be cleaned up, then hey, maybe the problems of both of our countries can cancel each other out a little!
See this alot among the Amish/Anabaptists here in the United States. There's no more farmland to be bought in the places they live, so each generation has the farm split between 4 and 6 sons, and they keep getting tinier. Until, at some point, it can no longer be divided. Moving and setting up a new colony elsewhere is difficult in the extreme, so it usually happens far past the point that it would make sense to split them (down to just a couple of hectares in many cases).
Sometimes when it's at its most extreme, they'll all take their pooled savings and go buy a square kilometer or two out west, but there aren't so many places like that left to buy, especially that are worth farming.
> So if countries like Japan want to attract immigration from here,
Here's another funny one about Japan. There is a not-well-known but peculiar class of potential immigrants. After (before?) a bunch of Japanese emigrated to Brazil. But, being Japanese, they didn't give up speaking Japanese. So they're more or less fully ethnically Japanese, speak the language as their first language, etc. And, as it turns out, many of them would be willing to move back to the land of their grandparents and great grandparents, if there were jobs.
Also, there are jobs!
So, the government initially sets up a program welcoming them back. But it turns out that they aren't welcome, either by elements in their own government, or society at large. They're simply too alien. Eventually, someone gets voted out, or retires out of government, the program is shut down, and those returnees are forced to go back to Brazil.
If Japanese society thinks those people are too alien, too foreign, to fit in... what chance do the Vietnamese have?