Why “Hare had even”
Not “Hare has even”

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The whole story is told in the past tense.
(Most stories are told in past tense)

"Had" is past tense. "Has" is present tense.

If the sentence was a quote of something that Big Nutbrown Hare said or exactly what he thought, then it would be
"But I have even longer arms," said Big Nutbrown Hare.
or
But I have even longer arms, thought Big Nutbrown Hare.

Since it is just the storyteller saying that Big Nutbrown Hare's arms were longer, it is in past tense.

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It is possible, but much less common, to tell a whole story in the present tense, but it is only done when the storyteller is IN the story, and still it is done for specific effect, to imply something about the storyteller's character.

I don't expect you will ever see it in a children's book.

In spoken speech, some people tell stories this way.

It is actually difficult to completely stick to present tense when telling a story, because the story did happen in the past.