You mentioned NH2 as a leaving group when talking about amines. But the leaving group would really be NH3, or RNH2, etc (a neutral leaving group). And alkoxides are more like "medium" leaving groups in this context. Still good enough to add reversibly.
In this video she posted, it looks like she is saying "milder" rather than soft or hard. She mostly references the pKa of the conjugate acid. The pKa of the conjugate acid is a good indication of whether the reaction is irreversible or reversible. It doesn't tell you directly about hard or soft properties. NaH for example is an extremely strong base, but also fairly soft because it only has one proton in the nucleus pulling on the electrons (naked H minus like this is usually just a base, however, and not a nucleophile).
Many texts will emphasize kinetics or only thermodynamics, when both aspects are actually important. In the video you referenced she says grignards only add 1,2, even though it is well documented that they sometimes have a preference for adding 1,4. This is a common "lie" they tell in Sophomore organic and it is best to just believe the lie at first, because remembering every case is very difficult.