The painting contains the formula to time travel.
As said by Auntie witch:
This painting was drawn hundreds
years ago in a time of war and famine.
Why did someone draw this painting when
the world was on the verge of destruction?
The most plausible answer to that question is that the painting contains the time travel formula.
Also, as seen in the movie Time Traveller: The Girl Who Leapt Through Time (2010), Auntie witch discovers the formula trying with different kind of herbs. The painting contains those herbs and the quantity needed.
In the first movie The Little Girl Who Conquered Time (1983), the time traveler says to Auntie witch that they are trying with different herbs to perfect the formula.
So, according to those facts, that is my answer. The painting contains the formula to time travel.