No one is truly debating this anymore in Finland. People who have lived in ceded Karelia have mostly died.

This ceased to be a real question decades ago. Virtually the original inhabitants living in the territory either fled to Finland or died in Stalin's gulags, since he specifically targeted politically suspect Karelians and Ingrians:

https://en.wikipedia.org/wiki/Genocide_of_the_Ingrian_Finns

What's left is a post-Soviet wasteland with no economy to speak of, thinly populated by migrants with no connections to Finland.

I've always thought that Russia should offer Finland a 99-year lease on a block of land that would extend Finnish administration to the NW shore of Lake Ladoga. We're talking a 35 km extension of Finland's border to a shoreline of about 80 km, well away from St Petersburg.

The arrangement would demilitarize the area. For example, upper limits on the number and size of Finnish police armament, and a right of unarmed Russian police to occasionally patrol the area.

Finns would move in, be horrified at the condition of Lake Ladoga, and immediately demand that the Finnish state fund a massive cleanup.

A win for Russia.

I have relatives from Karelia, Finland not even have a program to immigrate back to Finland.

Since Russia wants to hold referendums in the invaded territories in Ukraine to ask the people whether they want to become Russian or stay in Ukraine, why not ask the inhabitants of Karelia whether they want their land to stay in Russia or switch to Finland?

After recent developments in Moscow, I suspect that many of them would be happy to become European citizens.