Add page layout tab icon picker (#19818)

Adds the ability to change the icon of a record page layout tab from the
side panel in tab edit mode, and sets a default icon for newly-created
record page tabs (no default for dashboards).

<img width="916" height="312" alt="Screenshot 2026-04-17 at 19 55 51"
src="https://github.com/user-attachments/assets/d9f57e89-d40d-483e-b508-5d7318df1ef5"
/>

packages/twenty-front/src/modules/page-layout/utils/__tests__/convertPageLayoutDraftToUpdateInput.test.ts

@@ -34,6 +34,7 @@ const makeTab = (
   id: string,
   widgets: PageLayoutWidget[],
   layoutMode?: PageLayoutTabLayoutMode,
+  overrides?: Partial<DraftPageLayout['tabs'][number]>,
 ): DraftPageLayout['tabs'][number] =>
   ({
     id,
@@ -44,6 +45,7 @@ const makeTab = (
     isActive: true,
     layoutMode,
     widgets,
+    ...overrides,
   }) as DraftPageLayout['tabs'][number];
 
 describe('convertPageLayoutDraftToUpdateInput', () => {
@@ -109,6 +111,26 @@ describe('convertPageLayoutDraftToUpdateInput', () => {
     expect(result.objectMetadataId).toBeNull();
   });
 
+  it('should propagate tab icon to the update input', () => {
+    const draft = makeDraft([
+      makeTab('tab-1', [], PageLayoutTabLayoutMode.GRID, {
+        icon: 'IconHome',
+      }),
+    ]);
+
+    const result = convertPageLayoutDraftToUpdateInput(draft);
+
+    expect(result.tabs[0].icon).toBe('IconHome');
+  });
+
+  it('should send null icon when tab icon is undefined', () => {
+    const draft = makeDraft([makeTab('tab-1', [])]);
+
+    const result = convertPageLayoutDraftToUpdateInput(draft);
+
+    expect(result.tabs[0].icon).toBeNull();
+  });
+
   it('should handle multiple tabs', () => {
     const draft = makeDraft([
       makeTab('tab-1', [makeWidget({ id: 'w1' })]),

packages/twenty-front/src/modules/page-layout/utils/convertPageLayoutDraftToUpdateInput.ts

@@ -59,6 +59,7 @@ export const convertPageLayoutDraftToUpdateInput = (
           id: tab.id,
           title: tab.title,
           position: tab.position,
+          icon: tab.icon ?? null,
           layoutMode: tab.layoutMode,
           widgets: widgets.map((widget, widgetIndex) => ({
             id: widget.id,