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it's крошечка
It is indeed in a fairytale Крошечка-Хаврошечка which is probably several centuries old but I think nobody uses it as an endearment anymore. Partially because of Russian translation of...

I think those endearments should not be used if people do not have deep relationships.
I also think not every girl would want to be compared to a bird in general.

Galochka/галочка also means a check mark, so better be avoided

I think there are only two bird-ish endearments in Russian that are more or less common:
птичка - means a birdy
ласточка - means a...

I think it would be offensive, because it is similar to a babbler/chatterbox