Update intent template to use a new enum for field inclusion instead of `intent_stage`

The `intent_stage` field has mostly been phased out, but some fields are included or excluded in the intent template based on this value. The template should discern which fields to display based on the type of intent, of which the old intent_stage field does not regularly map to. This will also make it much easier to track which fields are part of which intents, and which are not.