Surprised me!

have you ever used your E-bike to haul anything? Does the bike allow you to pedal while it gives an assist up hills?

Yes, a bicycle trailer and yes, you can assist at any time. Some bikes even have a torque sensing system so it only supplies power if you are actively pedalling. Some you just let the throttle determine that speed and help out when you want.
My favorite is setting the cruise control (Yes, some have that) and pedaling cut down on the power needed for that speed, you can sometimes double your range that way.

ETA, we have a lot of Amish down here. They are all over on their tricycles, you know the full size ones with the big cargo basket on the back. Many, I would say most are electric powered. I have no idea how they justify it but then again the rider tends to be rather old. 60-70+.

Oh, real Amish, not arfcom amish....

I did a review of my ebike here: https://www.ar15.com/forums/outdoors/I-Bought-One-of-the-Cheapest-E-Bikes-on-Amazon-and-After-Several-Months-I-Am-Still-Enjoying-It-/1-699848/?r=-1&page=1&anc=11995730#i11995730

This thread mentions the different drive modes as well as the performance while pulling a trailer full of cargo.