Hello Rob H - CO,
Thanks for using Apple Support Communities. It sounds like you’re looking to have badge notifications on for your apps. I’m happy to help.
You should still have the option for “badges” in your notification settings in iOS 13. You can find steps below:
Use notifications on your iPhone, iPad, and iPod touch - Apple Support
On your iPhone, you’ll want to tap Settings > Notifications > [App] and make sure “Allow Notifications” is enabled. From there you should have the option to select “Badges.”
For Mail specifically, if you have more than one account, you’ll have to tap each account before you see that option.
Let me know if that helps.
Take care.