Not every Mac running High Sierra can handle Catalina. Apple dropped support for several older machines due to the requirement for Metal-capable graphics processors (GPUs).
Once the download finishes, the installer should open automatically.
If you open System Preferences > Software Update on High Sierra 10.13.6, you might see "Your Mac is up to date." This is because Apple's CDN (Content Delivery Network) often deprecates upgrade paths for older OS versions.