New room list: add search section (#29251)

* feat(new room list): move `RoomListView` to its own folder and add styling

* feat(new room list): add search section

* test(new room list): add tests for `RoomListSearch`

* test(new room list): add tests for `RoomListView`

* test(e2e): add method to close notification toast to `ElementAppPage`

* test(e2e): add tests for the search section

* test(e2e): add tests for the room list view

* refactor: use Flex component

* fix: loop icon size in search button

* refactor: remove `focus_room_filter` listener

res/css/_components.pcss

@@ -269,6 +269,8 @@
 @import "./views/right_panel/_VerificationPanel.pcss";
 @import "./views/right_panel/_WidgetCard.pcss";
 @import "./views/room_settings/_AliasSettings.pcss";
+@import "./views/rooms/RoomListView/_RoomListSearch.pcss";
+@import "./views/rooms/RoomListView/_RoomListView.pcss";
 @import "./views/rooms/_AppsDrawer.pcss";
 @import "./views/rooms/_Autocomplete.pcss";
 @import "./views/rooms/_AuxPanel.pcss";

res/css/views/rooms/RoomListView/_RoomListSearch.pcss

@@ -0,0 +1,39 @@
+/*
+ * Copyright 2025 New Vector Ltd.
+ *
+ * SPDX-License-Identifier: AGPL-3.0-only OR GPL-3.0-only OR LicenseRef-Element-Commercial
+ * Please see LICENSE files in the repository root for full details.
+ */
+
+.mx_RoomListSearch {
+    /* From figma, this should be aligned with the room header */
+    height: 64px;
+    box-sizing: border-box;
+    border-bottom: 1px solid var(--cpd-color-bg-subtle-primary);
+    padding: 0 var(--cpd-space-3x);
+
+    svg {
+        fill: var(--cpd-color-icon-secondary);
+    }
+
+    .mx_RoomListSearch_search {
+        /* The search button should take all the remaining space */
+        flex: 1;
+        font: var(--cpd-font-body-md-regular);
+        color: var(--cpd-color-text-secondary);
+
+        span {
+            flex: 1;
+
+            kbd {
+                font-family: inherit;
+            }
+        }
+    }
+
+    .mx_RoomListSearch_explore:hover {
+        svg {
+            fill: var(--cpd-color-icon-primary);
+        }
+    }
+}

res/css/views/rooms/RoomListView/_RoomListView.pcss

@@ -0,0 +1,12 @@
+/*
+ * Copyright 2025 New Vector Ltd.
+ *
+ * SPDX-License-Identifier: AGPL-3.0-only OR GPL-3.0-only OR LicenseRef-Element-Commercial
+ * Please see LICENSE files in the repository root for full details.
+ */
+
+.mx_RoomListView {
+    background-color: var(--cpd-color-bg-canvas-default);
+    height: 100%;
+    border-right: 1px solid var(--cpd-color-bg-subtle-primary);
+}