After completion, reboot and download iTunes from Method 1 again.
in macOS Catalina (10.15) and all subsequent versions, such as Big Sur, Monterey, and Sonoma. The Core Issue: Why iTunes Won't Install Itunes Macos 10.13.99 Download Fix
💡 If you still see update prompts for iTunes, ignore them. Apple has ended support for iTunes on macOS 10.13. Consider upgrading your Mac to a patched version of Catalina or newer via OpenCore Legacy Patcher if you need modern Apple Music or TV apps. After completion, reboot and download iTunes from Method