first birthday of a child
晬 centers on a child's first birthday, marking the completion of one full cycle of life.
晬 combines 日 (sun, day) with 卒, which likely contributes the sound and the idea of completion, together suggesting the completion of a full year cycle.
The sun 日 on the left and 卒 (soldier, but here suggesting completion) on the right: imagine a child completing its first full trip around the sun, celebrating its first birthday.
For サイ, picture a child's first birthday party with a big sigh of relief from the parents: sigh -> サイ, as they celebrate completing one year.