Ringtone deleting in IOS 13

I was able to delete ringtones in iOS 13 through the Clock app. Go to Clocks > Alarm and then either create a new alarm or edit a current one. Under Sound it lists all tones and you can swipe left the custom tones you want to remove. It should have a Delete option with the swipe.

Note this was under "Manually manage music and videos" selected with iTunes. I don't know if that makes a different here.

Use iTunes to delete custom tones that you manually added to your iOS device

If you manually added custom tones to your iOS device, you can delete them from your device using iTunes.

1. Connect your device to your computer.
2. Open iTunes. Make sure that you have the latest version.
3. Click your device in the left sidebar, then click Tones.
4. Control-click or right-click the tone that you want to delete, then click delete tone.