"Nya" is actually the definite form in this sentence. The definite form is usually the same as the plural form.
The definite form is used when a noun is definite, like in "Den nya idén" - "The new idea"
It's also used with possesive pronouns like "Min/Din/Vår/Er/Sin nya idé"
Astrid really messes up on pronouncing "Hon" here when the sköldpadda is clicked. You can barely hear it.
The plural form (here "nya") of the adjective (here "ny") is used with the definite form and with possessives:
en ny idé
den nya idén
min/din/sin/vår/er/deras nya idé
Because the subject of the sentence is "Hon".
"Sin/Sitt/Sina" always always ALWAYS refers back to the subject of the sentence.
"She thought of her new idea" is silly in English. It really doesn't make sense.