Can I set different sounds for different alerts on Apple Watch?

I know the sound settings in Settings | Sounds & Haptics and then they have Ring Tone and Text Tone etc., but there's a Default Alert that goes off for everything else and I'd like to be able to change that for different alerts, such as a particular sound when the iPhone battery is low.

So many things are customizable, then someplace you need one to be customizable and it's not, unless I'm missing something.

Thank you.

[Re-Titled by Moderator]

Original Title: Apple Watch - is there a way to set different sounds for different alerts?