Technically, the status field is not color-coded, it’s just that the Kanban GUI allows to change the color of the column, but there is currently no way to define a “per-object” color.
Every Kanban board in Frappe / ERPNext will display the documents’ list as the boxes you mentioned. Here, they are “Issue” documents.
The good thing with this feature is that it uses the Kanban default behavior (display color field if exist) and you can define with your team the “meaning” of each color ie. no hard-coded color mapping.