I’m not usually a believer in these “small upgrades,” but my neighbor swears her new front door cut her energy bills. Is that even possible or is it just a visual improvement?

You'd be surprised how much impact it can have. I live in Ontario where winters can be brutal. My old door had visible gaps and let in icy air. After some research, I ended up choosing https://www.elegantentrydoors.ca/front-door/ front doors designed specifically for Canadian weather conditions. The seal is so tight now that even during a windstorm, there’s zero draft inside. The real proof came with my heating bill — it actually dropped, and not just by a few dollars. If you think of the door as part of your insulation envelope, it really makes sense.