Is there a way to retrieve the type of an entry?
The structure type is stored in the section, not in the entry type. entry.type doesn't return the name, it returns the entry type as an object

{% set structureType = entry.getSection().type %}


It will return a string that can have the following values. 

const TYPE_SINGLE = 'single';
const TYPE_CHANNEL = 'channel';
const TYPE_STRUCTURE = 'structure';