Shapes's page

It's directly stated in the spells if they are battle forms. Untamed Form refers to other spells, so you look at them. If you're using Untamed Form to use the forms from Pest Form, Pest Form states "battle form" in the text. Same for Animal Form.

The Anthropomorphic Shape feat lets you use the effects of Humanoid Form. When you read the Humanoid Form spell, it does not say "battle form."

There isn't a more subtle sign or ambiguous interaction that you need to look out for.

Thanks for the pointer.

What distinguishes whether the form you choose is a "battle form" and, therefore, whether you can or cannot cast in that form? For example, I assume if I use untamed form to become a dwarf, I could still cast. Either I cannot find the clarification in the Player Core or the rules are ambiguous.