Why don't you go to Amazon and look up Frogg Toggs rain pants?
They're quite inexpensive. They're also very, very light. They'll pack up into a small package. Though you'll no doubt want to dry them first.
They're warm, too. I can ride in zero deg F weather with just these pants plus sweat pants beneath. I'm comfortable. If you don't deal with freezing temps, then you're likely to be just fine with these plus gym shorts beneath.
I go with just Froggs and gym shorts above about thirty five deg F. And I might experiment with going down to thirty or so dressed like this.
Also, you don't end up looking like a total fool. It looks about like baggy, black work pants.
Wait a minute.......did you say electric bike? Then maybe you don't want just gym shorts under these. But you'll still burn some calories on an electric bike. So sweat pants might be a bit too warm under some circumstances. Blue jeans might bridge the gap.