fix: Updating widget tree item props to show the correct icon for child widgets (#39605)

## Description

Updating widget tree item props to show the correct icon for child
widgets.

Fixes [#39602](https://github.com/appsmithorg/appsmith/issues/39602)

## Automation

/ok-to-test tags="@tag.IDE"

### 🔍 Cypress test results
<!-- This is an auto-generated comment: Cypress test results  -->
> [!TIP]
> 🟢 🟢 🟢 All cypress tests have passed! 🎉 🎉 🎉
> Workflow run:
<https://github.com/appsmithorg/appsmith/actions/runs/13700282344>
> Commit: d67f80f838cdd01bf738bed3eea832d86c038a0c
> <a
href="https://internal.appsmith.com/app/cypress-dashboard/rundetails-65890b3c81d7400d08fa9ee5?branch=master&workflowId=13700282344&attempt=1"
target="_blank">Cypress dashboard</a>.
> Tags: `@tag.IDE`
> Spec:
> <hr>Thu, 06 Mar 2025 14:24:55 UTC
<!-- end of auto-generated comment: Cypress test results  -->


## Communication
Should the DevRel and Marketing teams inform users about this change?
- [ ] Yes
- [ ] No


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

- **New Features**
- Enhanced the entity explorer by introducing an optional `type`
classification for each tree item, enabling more detailed visualization.
- Improved icon rendering in widget items by basing visual updates on
each item's `type`, ensuring a consistent display across the interface.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

app/client/packages/design-system/ads/src/Templates/EntityExplorer/EntityListTree/EntityListTree.stories.tsx

@@ -34,18 +34,21 @@ const Tree: EntityListTreeProps["items"] = [
     isExpanded: true,
     isSelected: false,
     name: "Parent 1",
+    type: "LIST_WIDGET",
     children: [
       {
         id: "1.1",
         isExpanded: false,
         isSelected: true,
         name: "Child 1.1",
+        type: "CONTAINER_WIDGET",
         children: [
           {
             id: "1.1.1",
             isExpanded: false,
             isSelected: false,
             name: "Child 1.1.1",
+            type: "IMAGE_WIDGET",
           },
           {
             id: "1.1.2",
@@ -53,6 +56,7 @@ const Tree: EntityListTreeProps["items"] = [
             isExpanded: false,
             isSelected: false,
             name: "Child 1.1.2",
+            type: "TEXT_WIDGET",
           },
         ],
       },
@@ -61,6 +65,7 @@ const Tree: EntityListTreeProps["items"] = [
         isExpanded: false,
         isSelected: false,
         name: "Child 1.2",
+        type: "TABLE_WIDGET",
       },
     ],
   },
@@ -69,6 +74,7 @@ const Tree: EntityListTreeProps["items"] = [
     isExpanded: false,
     isSelected: false,
     name: "Parent 2",
+    type: "BUTTON_WIDGET",
   },
 ];
 

app/client/packages/design-system/ads/src/Templates/EntityExplorer/EntityListTree/EntityListTree.test.tsx

@@ -21,6 +21,7 @@ const defaultProps: EntityListTreeProps = {
       isSelected: false,
       isDisabled: false,
       name: "Parent 1",
+      type: "CONTAINER_WIDGET",
       children: [
         {
           id: "1-1",
@@ -29,6 +30,7 @@ const defaultProps: EntityListTreeProps = {
           isDisabled: false,
           name: "Child 1.1",
           children: [],
+          type: "TABLE_WIDGET",
         },
       ],
     },
@@ -61,6 +63,7 @@ describe("EntityListTree", () => {
           isDisabled: false,
           name: "No Children Parent",
           children: [],
+          type: "TABLE_WIDGET",
         },
       ],
     };
@@ -84,6 +87,7 @@ describe("EntityListTree", () => {
           isSelected: false,
           isDisabled: false,
           name: "Parent 1",
+          type: "CONTAINER_WIDGET",
           children: [
             {
               id: "1-1",
@@ -92,6 +96,7 @@ describe("EntityListTree", () => {
               isDisabled: false,
               name: "Child 1.1",
               children: [],
+              type: "TABLE_WIDGET",
             },
           ],
         },

app/client/packages/design-system/ads/src/Templates/EntityExplorer/EntityListTree/EntityListTree.types.ts

@@ -5,6 +5,7 @@ export interface EntityListTreeItem {
   isDisabled?: boolean;
   id: string;
   name: string;
+  type: string;
 }
 
 export interface EntityListTreeProps {

app/client/src/pages/AppIDE/components/UIEntityListTree/UIEntityListTree.tsx

@@ -18,6 +18,7 @@ export const UIEntityListTree = () => {
     name: widget.widgetName,
     isSelected: selectedWidgets.includes(widget.widgetId),
     isExpanded: expandedWidgets.includes(widget.widgetId),
+    type: widget.type,
   }));
 
   return (

app/client/src/pages/AppIDE/components/UIEntityListTree/WidgetTreeItem.tsx

@@ -68,8 +68,8 @@ export const WidgetTreeItem = ({ item }: { item: EntityListTreeItem }) => {
   );
 
   const startIcon = useMemo(
-    () => <WidgetTypeIcon type={widget?.type} />,
-    [widget?.type],
+    () => <WidgetTypeIcon type={item.type} />,
+    [item.type],
   );
 
   const onClick = useCallback(