sprout, flourish, vigorous
茁 centers on vigorous new growth: a sprout emerging strongly and flourishing. The idea is one of lively, healthy development.
茁 combines 艹 (plant) with 出 (to come out), suggesting a plant emerging from the ground. This is a straightforward semantic-component explanation.
Plants 艹 coming out 出 of the soil: that is a sprout, growing vigorously and flourishing.
For サツ, imagine a sprout shooting up so fast it makes a sharp 'satsu' sound as it breaks the surface: satsu -> サツ.