Mystery chain issue

[Koi Fish]

Background: Recumbent catrike with NuVinci N380 hub, Bafang Ultra motor, and upgraded (TerraTrike?) idler.

I'm getting some really weird tension or popping on my chain. Like, when you are using a normal cassette and your chain doesn't fully move to a cog... it 'snaps' after some pushing on the pedals or when I'm giving it throttle. This normally happens after either shifting or changing PAS levels and it gets more common on hills - normally because I'm shifting and or changing PAS levels. It's loud and doens't sound good and looking at the drivetrain, I don't see anything that could be causing this tension snapping. Am I doing something wrong or does anyone have experience with this? Looking for more info on this weird issue.

 

[indianajo]

It can't be mis-adjustment of the derailleur because you don't have one.
Step one is to measure chain wear with a gauge. I used the Park one. To make this measurement valid the measured links must be under tension.
If okay, next is to take out a link if possible. Chain line mis-alignment could be at fault. Least likely is a worn out small sprocket. Look & see if the tips are round.
I wore the tips off the middle sprocket of a 5 speed rear cluster in 15 years. Since they quit selling 5 speed rear sprockets at the end of that time, I had to scrap the bike.

 

[Koi Fish]

Thanks for the recommendations, I'll be checking those asap!