
Calth |
They would probably fall under the animated object rules at that point and be considered constructs. Basically, PAO is a way to animate an object. And all objects that are animated are covered by the specific Animated Objects bestiary entry (the entry states that all objects, however they are animated, fall under it). And Animated Objects are constructs.

The Imperator |

Except that it specifically says you can turn a rock into a human. Not into a construct, which could be permanent (large rock -> large construct/no Int/same kingdom(mineral)) going by the listed rules. Thus making PAO strictly better than animate object. All you need is the spell to control a construct, and you are set for animated objects for virtually no cost.

Calth |
Except that it specifically says you can turn a rock into a human. Not into a construct, which could be permanent (large rock -> large construct/no Int/same kingdom(mineral)) going by the listed rules. Thus making PAO strictly better than animate object. All you need is the spell to control a construct, and you are set for animated objects for virtually no cost.
But you don't turn fully rock into a human, because that's not what the spell does, because polymorphs don't change types. PAO changes forms only. And the Animated Object bestiary entry says it covers all objects that become animated, with the animate object spell being one way. PAO should be another if you are turning an object's shape into an animate form.

Calth |
I would have thought it better to keep it as typeless. Construct type comes with all sorts of baggage that might cause more confusion than it clears.
Except you can't really do that. The Animated Object Bestiary entry is pretty broad as it basically states that it covers all objects animated by any means besides craft construct. In effect it means that objects have a hidden type of construct. That is they normally aren't creatures but if they somehow become one they are constructs, which is reasonable and consistent.
It's not necessarily the simplest method but it seems to be what the rules are.