Why does anyone let non-resident people buy residential housing?
Why does anybody limit supply of housing to the point that prices rise?
The French did a bad job at building satellite cities, but done right, you could connect new housing to the city center like the original Los Angeles street cars.
If jobs don't pay much then you also don't pay much to the builders of new houses which makes them affordable.
The desirable locations are a renewable resource. Portugal could build new desirable areas. They could even turn this into a recurring business and sell them to international investors, too. Instead of building suburban sprawl they can build more urban clusters.
Things will probably shift when the proportion of renters significantly outnumber the home owners.