There [he/she/it] is!
is an exclamation that you have found something you were looking for. The speaker was probably wondering where she was, or at the least talking about her, when she appeared.
The reason it's not listed in the dictionaries is that, although it's a common phrase, it's not a "special" phrase - it's just a normal grammatical construction and its meaning is derived from the meaning of the constituent parts:
There (location) he (subject) is (verb to be) !
The emphasis is usually on there because you're emphasizing that you didn't know the location of the person (or object) and now you've found it: he/she/it is there.
There you are!
can also be used in this way. It means, "I was looking for you and now I've found you" or "I wondered where you are, but now you've appeared." You wouldn't say it in the middle of a conversation; you'd say it at the start.
However, there is another meaning of There you are!, which is the one you found. It's not more common, it's just that the phrase itself has a particular meaning beyond the definition of the individual elements, and so it's more necessary to define it.
Here I am!
would be the equivalent for the first person. (You can't say "There" because the here/there distinction is relative to the speaker.)
It has a similar meaning: you are announcing your arrival because you believe everyone was expecting you somehow - either looking for you, or waiting for you, or something similar.