Have you driven 100+ miles on a single charge with your new battery, or does the range guess-o-meter tell you that you have 100+ miles of range? The range estimate is strongly weighted by recent driving.
As an example, our 2014 SV with 77K miles on the original 24 kWh battery (11 SOH bars) provides a range guesstimate of 95-100 miles when fully charged at my wife's work. Why? The last few miles of her drive to work are downhill (30-40 mph speed limit) and then flat (30 mph speed limit), both situations where the Leaf is very efficient.
When you set out from her place of work headed home, the guesstimate drops from 95-ish miles to 65-70 miles over the first 3-4 mostly uphill miles of the trip. Once the road becomes more rolling the estimated range starts to increase again (up to 80-85 miles) and then drops slowly over the remainder of the 17 mile drive home. She arrives home with 78-80% charge and a range estimate of 70-75 miles. Our overall efficiency (5.3 miles/kWh over about 17K miles and 2.5 years of ownership) is helped by our driving conditions: rolling, mostly rural roads with low (25-45 mph) speed limits. Pretty much the ideal scenario for maximizing the range of a first-generation Leaf.
The best way to figure out what capacity battery they installed, and the condition of that battery, is to ask the dealership(?) that did the install.
