When is it safe to wipe and delete old device so the new device works properly

You can use the following procedure to clear your old iPhone and it will not affect iCloud or your new iPhone: What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

But iCloud should be able to backup your new iPhone whether or not you have done that yet. If you are having an issue with lack of space on iCloud (or even if you’re not) you can erase the backup of the old iPhone on iCloud to free some space. See instructions in the backup section of Manage your iCloud storage - Apple Support

Yes. Once you have transferred your data to your new device, you can safely erase the old device and backup with iCloud. Backing up has no bearing on whether you erase the old device or not. Each device backup is independent and has no bearing on another device.