[Risolto] WPML Custom post type translation is not showing the right slug

Background of the issue:
I am trying to change the IT slug of my custom post type (CPT) but it's showing the wrong slug. The issue can be seen on this page: link nascosto

Symptoms:
I expect to see the slug called 'projects', but instead, I see the old slug called 'inspiration'.

Questions:
How can I change the IT slug of my CPT to 'projects'?
Why is the old slug 'inspiration' still showing instead of the new one?
Also do I need to add the Italian labels in my code? Because it should be 'progretti'.