Fix Tree Quick Pick sticky scroll background color mismatch (microsoft#259586)

* Initial plan

* Fix Tree Quick Pick sticky scroll background color mismatch

Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>

---------

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>
Co-authored-by: TylerLeonhardt <2644648+TylerLeonhardt@users.noreply.github.com>

Author: Copilot

src/vs/platform/quickinput/browser/quickInputController.ts

@@ -881,6 +881,7 @@ export class QuickInputController extends Disposable {
 			this.ui.container.style.border = widgetBorder ? `1px solid ${widgetBorder}` : '';
 			this.ui.container.style.boxShadow = widgetShadow ? `0 0 8px 2px ${widgetShadow}` : '';
 			this.ui.list.style(this.styles.list);
+			this.ui.tree.tree.style(this.styles.list);
 
 			const content: string[] = [];
 			if (this.styles.pickerGroup.pickerGroupBorder) {

src/vs/platform/quickinput/browser/quickInputService.ts

@@ -240,6 +240,7 @@ export class QuickInputService extends Themable implements IQuickInputService {
 				listInactiveFocusBackground: quickInputListFocusBackground,
 				listFocusOutline: activeContrastBorder,
 				listInactiveFocusOutline: activeContrastBorder,
+				treeStickyScrollBackground: quickInputBackground,
 			}),
 			pickerGroup: {
 				pickerGroupBorder: asCssVariable(pickerGroupBorder),