It’s a private repo but it’s not in a github organization. I shared the project with the Github owner account to the other account connected to Vercel.
I tried to create a Test project with the github account connected to Vercel and it appears in the list as you can see on the photo below, but the other project is not shown.
It seems that if the github account is not the owner of the github project, but anyway it has full access, Vercel can’t import correctly project.