July 2020
I am having the same experience. Using the Nano trash can while Off-the-Grid trait is applied to lot and no power stored/generated results in the sim picking up the trash and then dropping it again. If Off-the-Grid trait is removed (and no other changes), it suddenly works. If Off-the-Grid trait applied and power stored/generated, it also works. Seems that the 'Works Off-the-Grid' label on the Nano trash can is not accurate and it needs power. I was kinda hoping it was battery operated *heh*
August 2020
I'm having the same problem. I have 0 power storage in my house and when I tell my sims to use the trash they pick it up, look in to the air and them let the trash in the ground again. Aparently it needs electricity, it's a shame, because I wanted the trash to generate power, not to use it.