How to represent the array of String in Entity Realtionship Diagram?
In a logical datamodel the array should be a separate table. It will have a foreign key referencing the table it is currently in.

In a physical model, from which DDL will be generated, showing it as an array is the right thing to do as this it the desired type for the column.

Neither is the "correct" representation. Each has a different purpose and is right for its own use.

Some modelling tools allow physical and logical representations to coexists in a single model and hold the mappings between them, some do not. If yours doesn't decide at what level you want to model and be consistent.