I have a new Pixel 6 Pro phone. I downloaded the Screen Care software to my phone. I got a message that my "iPhone 6 is now protected". I didn't see any place to delete my old iPhone 6 first.
Are you still using 360 on the iPhone? If so, I would suggest temporarily uninstalling 360 iOS. Then go into your Norton Account and click on the user icon at the top right and then click on Manage My Subscriptions. Find your current 360 subscription and click on Manage Licenses. Find the iphone and click the trash can beside it to remove that activation.
Then go back to your new Android phone and go to Android Settings > Apps and look for the Screen Care app. Tap that and look for the Storage section. Tap that and then clear the App Data. Open the Screen Care app again and see if it will pick up your new phone.