As of 12/10/2020, Deep Links are not supported for use within the new email editor. Call to Action (CTA) buttons currently only support opening a website, sending an SMS, sending an email, or making a phone call. A Deep Link example would look like https://dl.punchh.com/deeplinks/<brand_slug>/account-history.
A workaround for this is creating a custom HTML content block to create a button for the Deep Link.
If further assistance is required, submit a ticket to Punchh Support. (For help submitting a ticket, click here)