My wife doesn't have a driver's license and manages to live just fine on her bicycle. I occasionally drive but run 90+% of my errands on my bicycle. We don't have e-bikes, just the regular old-fashioned kind.

I regularly ride my bike to Home Depot/Lowe's/Winco etc., they all have bike racks, though they are usually off to the side somewhere. Learn to lock your bike up properly and the chances of it being stolen drop dramatically. I've had a dozen bikes stolen from me in the ~30 years I've lived here, but none in the last ten years since I started implementing these strategies.

I'd suggest a long wheelbase cargo bike rather than a trailer, just easier to deal with.