In your own words, what is the relationship between the fish swimming to the paper and swimming to the heart? Which idiom story does this relate to?

Related to the idiom "Be confident".

The fact that the fish swam onto the paper shows that the fish was painted as lifelike as if it were alive. If you want to draw fish so vividly, you need to observe carefully and practice hard. Only when you have fish in your heart can you draw good fish, that is, the fish swims in your heart.

So first the fish swims to the heart, and then the fish swims to the paper.

Confident, a metaphor for being skilled and confident. Only when you have bamboo in your heart can you draw good bamboo. This is exactly the same as the only way to draw good fish is to have a fish in your heart.

So it is related to having a confident mind (also made into a confident person).