I think “genocide” is appropriate here - it’s a group of people, selected because of a shared trait that were mass murdered.
The first sentence I think covers it: “A campaign of mass murder” states what it actually was, and “by involuntary euthanasia in Nazi Germany” states what the Nazis claimed it was.
To the Right, only the in-group should be alive at all. Everyone not in the in-group is a waste of resources. It’s important that we understand this, as it’s the same thing now as it was in the 1930s and 1940s. To them, “mercy killing” meant merciful to the Nazis and care takers. It meant that it removed the burden on them of the people they didn’t desire.