This is mostly my fault, but it seems worth mentioning - at a minimum to set my expectations, and it could be a bug.
I created an Azure WebApp that was intended to be an Azure Function. I did the pulumi up, and from pulumi's POV, everything looked right. However, in the Azure portal, it just showed as a regular "app service". Checking my code, I see that I forgot to set the "Kind" property to "FunctionApp" (sort of a big deal - I know).
So I added the property, and pulumi preview said it would update based on that property change. However, when I ran "pulumi up," though it thinks it succeeded, the portal still shows it as an "app service." And the template shows that the value of "kind" is "app."