First time I hear of webP animations. But I was intrigued so I did some research.
I found that to make the animation loop it needs this bit of code: -loop 0
After a few attempts I found out how to export an infinite webP loop in Shotcut:
In the Export tab, choose the WebP Animation preset in the presets list.
Click the Advanced button.
In the Other tab, add loop=0 at the bottom of the list.