When working with Ideas directly in Aha! (not via the Ideas portal) there is a discrepancy with how the Tags field works.
On the Create ideas form, the Tags field does not allow you to add new values (see attached Create Idea Tags field no results and can't add.png)
However, on the Edit form, the same Tags field does allow you to add new values (see attached Existing Idea Tags field no results and can add.png).
According to Aha! support issue 860063 this was acknowledged as the "current behavior" but a specific use case explaining why there is a discrepancy in how the same field works could not be provided. The recommendation was to open a new Idea to evaluate this further.
The suggested resolution for this would be to update the Create ideas form so that the Tags field allow you to create new values as it does on the edit form.