I live about 3 miles out of town, fortunately directly on a rail trail. I ride my e-bike in to town to get groceries weekly. I have saddlebags on the bike and I pull a kids trailer with the seat folded down and have never run out of room, or had issues with weight. Sometimes I'll even get a few bags of water softener salt. I have a fat tire ebike (aventon), it's pretty sturdy. I've got about 2k miles on the bike, I'd guess half those are from grocery runs.
Pleaser tell me that the bike trail is off road and unpaved.