When fields in a datatype are changed to a picklist type and referred to a datapage and property value, the fields in the datapage are not displaying as dropdowns but remain as text properties.

Dynamic dropdown in data type | Support Center

We can observe the same behavior in delegation in the end-user portal, which is not allowing users to select the input but instead requires them to enter text.

Is there any way to achieve this through a local workaround for delegation?