There's no need for the repo owner do anything: they already indicate the license. GitHub even shows a simple explanation of the license in the repo's main page. GitHub has all the data it needs to respect the license. If their trained model can't reproduce the license for the repo a fragment comes from, then they've failed in their social and legal responsibilities.

It would actually be great for everyone if it showed both the license and repo. Imagine you pull up a great function with Copilot and want to explore the source for more insights. You can't with how they've done this.