Set background of Input Mode Widget (#6741)

Task/Issue URL:
https://app.asana.com/1/137249556945/project/1200204095367872/task/1211244094853968?focus=true

### Description
- Fixes an issue where content is visible behind the input when
scrolling under certain scenarios.

### Steps to test this PR

- [x] Fresh install
- [x] Submit “hello" search query
- [x] Tap the omnibar again
- [x] With the “Same privacy…” card visible, scroll up
- [x] Verify that the content does not scroll under the Input Mode
Widget

Author: joshliebe

duckchat/duckchat-impl/src/main/res/drawable/input_mode_widget_background_gradient.xml

@@ -0,0 +1,14 @@
+<?xml version="1.0" encoding="utf-8"?>
+<layer-list xmlns:android="http://schemas.android.com/apk/res/android">
+    <item>
+        <shape>
+            <gradient
+                android:angle="270"
+                android:centerColor="?attr/daxColorBackground"
+                android:centerY="0.8"
+                android:endColor="@android:color/transparent"
+                android:startColor="?attr/daxColorBackground"
+                android:type="linear" />
+        </shape>
+    </item>
+</layer-list>

duckchat/duckchat-impl/src/main/res/layout/fragment_input_screen.xml

@@ -25,7 +25,6 @@
         android:id="@+id/inputModeWidget"
         android:layout_width="0dp"
         android:layout_height="wrap_content"
-        android:layout_marginTop="@dimen/keyline_2"
         android:elevation="1dp"
         app:layout_constraintEnd_toEndOf="parent"
         app:layout_constraintStart_toStartOf="parent"

duckchat/duckchat-impl/src/main/res/layout/view_input_mode_switch_widget.xml

@@ -2,11 +2,22 @@
     xmlns:app="http://schemas.android.com/apk/res-auto"
     android:theme="@style/Widget.DuckDuckGo.ToolbarTheme">
 
+    <View
+        android:id="@+id/backgroundLayer"
+        android:layout_width="0dp"
+        android:layout_height="0dp"
+        android:background="@drawable/input_mode_widget_background_gradient"
+        app:layout_constraintTop_toTopOf="parent"
+        app:layout_constraintStart_toStartOf="parent"
+        app:layout_constraintEnd_toEndOf="parent"
+        app:layout_constraintBottom_toBottomOf="parent" />
+
     <com.duckduckgo.duckchat.impl.inputscreen.ui.view.InputModeTabLayout
         android:id="@+id/inputModeSwitch"
         style="@style/Widget.DuckChat.TabLayout.Rounded"
         android:layout_width="wrap_content"
         android:layout_height="@dimen/inputModeSwitchHeight"
+        android:layout_marginTop="@dimen/keyline_2"
         app:layout_constraintStart_toStartOf="parent"
         app:layout_constraintEnd_toEndOf="parent"
         app:layout_constraintTop_toTopOf="parent"