just over 6 miles. some climbes not that steep long. rest is fairly flat
What’s your fitness like? As mentioned your commute sounds well within the scope of a normal bike.
However I'm not posting to put you off the idea of an ebike, I think they're a fantastic invention.
I spent a few years commuting on my non electric hybrid but the last mile up the hill on the way home was really putting me off. I'd be knackered by then and I was struggling to maintain 6mph at the steepest bit, often with strong headwinds, and with rush hour traffic and having to pass parked cars at little more than walking pace I didn't feel safe. The e-bike was the answer and getting one was one of the best things I've done.
I've now got two, an Orbea Gain e-road bike with the Mahle rear hub motor and a Cube Reaction hardtail e-MTB, with the Bosch Performance Line motor. I've got the Cube kitted out with rack and mudguards as a do anything machine. Two very different beasts though.
The Gain weighs something like 15-16kg and a claimed 44nm torque and the Cube 25+ but a claimed 85nm. The Bosch motor also has the ability to temporarily "overboost" while still remaining legal as the motor is rated to 250w continuous. It certainly shifts you in turbo or e-mtb mode and is no slouch in the lower modes either. But the weight and the heavy knobbly tyres make it a pain to go above 15 mph unless downhill so you tend to go everywhere at 15. On the Gain as it's lighter with road tyres and lower torque, I often don't notice the cutoff unless I'm going up a steep hill. It's a much more fun ride on tarmac, but the Cube is obviously more fun off road.
You have to put more effort in with the Mahle system, but it's still a welcome boost. Depends on your weight and fitness but on a 10-12% I'd have no problem on the Gain on L2 or L3 assistance, but above 16% or so does get quite hard even on max. The Cube I've cycled up 20% gravel ramps and it felt like getting a tow from a ski-lift!
If I could only have one e-bike I'd probably have a hybrid with the Mahle hub motor, like the Orbea Vibe or Raleigh Trace.