cy.intercept is one of the most used commands in real Cypress work, and it is a main reason teams pick Cypress for apps with a busy API. You cannot run it in the editor on this site, because our browser engine does not implement request interception. Everything below is real, working Cypress. Use it on a local project and it behaves exactly as described.
Here is a bug that a normal test will never catch.
You create a contact named Dana Fox at the company FoxLabs. The green message appears. The new row appears in the table. Everything looks correct.