Well, spirits clearly aren't unchanging the way (in theory) the gods are. That 5% POW gain seems to indicate that they can improve, but also that it's very slow, as they're not active the the material world. I think it's cool to give them skill checks (perhaps also capped to 5% chance of success?) and that capped POW gain roll, but probably not occupational experience.
I would imagine that most spirit cults are fairly old, just as an example. This means that at least in some regard, the spirit is old (it has been worshipped for that long, regardless of what its subjective time felt like).
That Sword spirit, what if it used to be a Raven spirit instead (assuming it works that way)? Then it might have a bunch of fun and useless skills. 🙂