I'm not getting sound notifications for text or emails on my smartphone, only get them on my gear S3 watch. This is a problem when I don't have my watch on. I won't know I have a text or email unless I'm always looking to my phone to see if there's a new message.
Not sure what you mean by "safe mode" plus you shouldn't have to be in "safe mode" for notifications to work on the phone. This notification problem is new perhaps from the last S3 update. The phone and watch always had different sounds notifying me. The ringtone on my phone still sounds along with the S3. It's just not notifying me of email or text messages
With the phone in safe mode, we can ensure that there is no third party application interfering with your notification settings. While your device is in safe mode it will disable all third party applications so we won't be able to test the email notifications however we can still test the text message ones.