Yup. When I was in South Africa, there used to be many advertisements for South Africans to buy property in Portugal (and other countries). If you spent $600,000 or more on a property, then you were granted instant immigraiton, and you could get a passport within five years. So when that kind of money is floating around, people in Portugal will increase the prices of their homes. Why wouldn't they?

That's what prices out the locals. There are golden visa programs

https://www.henleyglobal.com/residence-investment/golden-visa