In later seasons it acts more like, well, a computer. Geordi does play (verbal) games with it in one episode, however, while bored on a shuttlecraft trip.
But I am mostly familiar with the later TNG era star trek, so I didn’t know it was written as self-aware in the early days.
Some episodes do feature “bugs” where holographic actors become aware being in a program/being an actor. The episode where an Irish town program has run too long on Voyager comes to mind.
(Edit: I do wonder if the holographic actors are somehow sandboxed containers in the main computer core, or run on a different system)
But I think the Star Trek writers just didn't understand computers very well. In the future, making duplicate copies of data seems to be impossible. When you copy a file from one device to another, or one ship to another, or transmit it to a planet, it seems to disappear from the source.
This is a particularly common weirdness in Voyager, where duplicating holographic programs is apparently impossible. You can only move them.
I.e. they went all in on c++ 11 and everything is an rvalue reference.
Maybe they figured out blockchain unique data structures that can’t be copied ;)