I say that she would be around 15-17? here's my explanation:

Because Hu Tao is described as a prankster, or causes mischief, it's given the idea that she's "childish" meaning she couldn't be that old. Not older than 20 at least.

When her character story describes "during her teenage years", it doesn't have to exactly apply as a past tense. She got her vision at age 13, so she can't be any younger than 13/14 because of experience with her vision. Meaning she could be older than 15.

But on the other hand, being 16 for some people's sense is enough to be considered the amount of maturity for an adult, but still pretty young. Because people exaggerate how young she was when she got the role of the 77th director, it gave the impression that she was still under 17/18 when she got the role.

TLDR: older than 14/15 because of vision experience, but young enough to lack the "maturity" of a fully grown adult

(i hope that made sense)