Preschool seems to be the word typically used for children’s education before they enter elementary school. But how do we call a child who has finished preschool education? Is it valid to use preschooled? I just Googled for this term and found no such usage.
In Britain we would say that they were a child of normal school age, (or of school age).
This would mean either that they had reached their fifth birthday (from when education becomes compulsory), or that they were a rising five and, depending on the local schools’ admissions criteria, were eligible for a school place.
Perhaps because there is no legal requirement for a child to be pre-schooled, though nowadays almost all children are, there would seem no requirement for a word which means ‘pre-schooled’.
A pre-school institution is usually, nowadays, called a day nursery. The word kindergarten, resonant of the private-school sector, is a bit old fashioned, nowadays.