Fix header z-index issues

packages/base-styles/_z-index.scss

@@ -25,7 +25,7 @@ $z-layers: (
 	".block-library-gallery-item__inline-menu": 20,
 	".block-editor-url-input__suggestions": 30,
 	".edit-post-layout__footer": 30,
-	".edit-post-header": 30,
+	".edit-post-editor-regions__header": 30,
 	".edit-widgets-header": 30,
 	".block-library-button__inline-link .block-editor-url-input__suggestions": 6, // URL suggestions for button block above sibling inserter
 	".block-library-image__resize-handlers": 1, // Resize handlers above sibling inserter
@@ -75,7 +75,8 @@ $z-layers: (
 
 	// Show sidebar in greater than small viewports above editor related elements
 	// but bellow #adminmenuback { z-index: 100 }
-	".edit-post-sidebar {greater than small}": 90,
+	".edit-post-editor-regions__sidebar {greater than small}": 90,
+	".edit-widgets-sidebar {greater than small}": 90,
 
 	// Show notices below expanded editor bar
 	// .edit-post-header { z-index: 30 }

packages/edit-post/src/components/editor-regions/style.scss

@@ -53,6 +53,7 @@
 	right: 0;
 	bottom: 0;
 	left: 0;
+	background: $white;
 
 	&:empty {
 		display: none;
@@ -63,22 +64,27 @@
 		overflow: auto;
 		border-left: $border-width solid $light-gray-500;
 		position: relative !important;
-		z-index: initial;
+		z-index: z-index(".edit-post-editor-regions__sidebar {greater than small}");
 	}
 }
 
 .edit-post-editor-regions__header {
 	flex-shrink: 0;
 	height: auto;  // Keep the height flexible.
 	border-bottom: $border-width solid $light-gray-500;
+	z-index: z-index(".edit-post-editor-regions__header");
 
 	// On Mobile the header is sticky.
 	position: sticky;
 	top: 0;
+
+	@include break-small() {
+		top: $admin-bar-height-big; // The top bar is fixed on this breakpoint.
+	}
+
 	@include break-medium() {
 		// Cancel the fixed positionning used in mobile.
 		position: initial;
-		overflow: auto;
 	}
 }
 

packages/edit-post/src/components/header/style.scss

@@ -8,7 +8,6 @@
 	align-items: center;
 	// The header should never be wider than the viewport, or buttons might be hidden. Especially relevant at high zoom levels. Related to https://core.trac.wordpress.org/ticket/47603#ticket.
 	max-width: 100vw;
-	z-index: z-index(".edit-post-header");
 
 	// Make toolbar sticky on larger breakpoints
 	@include break-zoomed-in {

packages/edit-widgets/src/components/sidebar/style.scss

@@ -13,7 +13,7 @@
 
 	@include break-small() {
 		top: $admin-bar-height-big + $header-height;
-		z-index: z-index(".edit-post-sidebar {greater than small}");
+		z-index: z-index(".edit-widgets-sidebar {greater than small}");
 		height: auto;
 		overflow: auto;
 		-webkit-overflow-scrolling: touch;