Fwiw, the logic is, “its” isn’t quite the equivalent of “Anna’s” or “school’s.”

Rather it’s the equivalent of “his,” “hers,” and “theirs.” Also “mine” but that’s just irregular af. In other words, possessive pronouns don’t take an apostrophe while possessive nouns do.

It’s not a LOT of logic, a pretty shaky ladder, but there it is.

(Oh, and for both nouns and pronouns, position in the sentence makes a difference whether to use a contraction at all, or go with the separate “is.” But that’s a horse of a different color!)