There are two approaches to start using the new cloud Platform. One approach is to use a Custom CNAME and cut over traffic using a DNS Switch. The other approach is to systematically change your build configurations to use the cloud Platform URL.
Any On-Prem specific configurations in your CI/CD builds should be updated before going live to ensure nothing goes wrong. If a few failed builds are acceptable, and you know which ones to update, begin updating them systematically during the cutover phase.