Probably more like 300Wh/mile. A Tesla Model 3 gets 4miles per kWh and that’s measured at higher average speed. At 3.3miles per kWh and 1.3kW for a typical L1 charger (literally just any standard 120V outlet), the average 45 mile range (13.5kW) would be charged in just 10 hours. With probably 14-16 hours charging each night, that's plenty to replenish greater than average usage as well. Put a 300 mile range battery in there, and you only need to charge once a week. (And note that the old Grumman LLV only had like 13.3 gallons and atrocious 10mpg, so that'd be like double the range and less frequent fuelings/chargings.)
At cruising speed, I assume? Delivery is going to be radically worse, because it has a ton of start and stop operation, the worst case for consumption.
You also seem to be spec'ing what it looks like for a post office to recharge one vehicle. What about dozens, plural? A current post office needs only marginally greater power than a residence. Charging dozens of electric vehicles is going to need more than that.
Roll down to your post office during off hours and count the number of trucks. I live in a very small city (people used to SF or NY wouldn't even call it a "city") and we've got dozens.
Not sure where you're getting the 1000Wh/mile number, but if it's from "normal driving" it won't apply. Mail delivery is stop and start, which is much worse. (If regenerative braking was 100% it'd be fine, but it's nowhere near that.)
I think you are all greatly underestimating how much damage it does to drive down a neighborhood, stopping every hundred feet, and re-accelerating. Cruising speed consumption is not a useful number here.
Since average mail route is 45miles [1]. At 1000Wh/mile - that's only 45kWh of charge needed per vehicle.
[1]https://www.grit.com/community/usps-rural-delivery-factoids