That's a really good question! I was wondering the same. I noticed that basically every postcard had one classic / older and one more modern / newer entry (the only noticeable exception being Australia for obvious reasons). I think the artist themselves might have selected some other things.
But because I got curious, I just looked it up and on the Eurovision website introducing the new format, they say

The Postcard will not only introduce the performers, but also the countries that each act is singing on behalf of. And this will also extends to the context of our participating broadcasters' most memorable moments at the Eurovision Song Contest. "We also added some public service – a graphic map to see where all the countries are located in the world. And then we wanted to celebrate the rich and incredible history of the Eurovision Song Contest by adding a couple of previous great entries from the Eurovision archives of each country."

It sounds to me like the EBU has a big influence and can determine how the selected videos should be. The national broadcaster might decide the specific country and ask if it's okay. But of course that's just my speculation.