Airtable forms are fairly limited. When people use the form they only see the primary field value for the linked record choices. If you want to show more information, you have to include that info in the primary field.
One solution is to move your date to a different field other than the primary field. Then turn your primary field into a formula field that combines the date and the label. You might want to use
DATETIME_FORMAT()for the date field in your primary field formula. It is documented in the formula field reference.