You have to enable two factor authentication to set up HomePod
Check that two-factor authentication is turned on for your Apple ID and iCloud Keychain is turned on
- To check if two-factor authentication is turned on, go to Settings > [Your Name] > Password & Security. If two-factor authentication isn't set up, select the option to enable it and follow the steps.
- To check if iCloud Keychain is turned on, go to Settings > [Your Name] > iCloud. Scroll down and check that Keychain is on. If it isn't, tap Keychain and turn it on. If prompted, follow the steps to set up iCloud Keychain.
See: If you can't set up HomePod - Apple Support
Im sorry, if you said you already did all this then just try signing out of iCloud or iTunes on your iOS device then sign back in. You need to be signed into your Apple ID to begin set up. Update your device to the latest software as well. Once you’ve set up the mini you should also update its software from the home app.