Install backup of my old Mac on my new one
You could use the Disk Utility to create a new APFS volume in your current APFS container. Next, download macOS Catalina from Apple App Store which will appear as the Install macOS Catalina application. Run this application and install Catalina in the new volume. Boot to the new volume and run the Migration Assistant application to transfer applications and data from the old Mac. This transfer is in the form of a copy. In other words, nothing is removed from the old Mac.