feat(chat): 채팅방 배경 사진 변경 기능 추가

- ChatRoomMoreDialog에서 배경 사진 변경 Picker 연결
- my-list API 추가 및 Repository 위임 추가
- 배경 선택 Dialog(3열 Grid, 4:5 비율) 및 선택 상태 UI 구현
- SharedPreferences로 roomId별 배경 URL 저장/로드
- ChatRoomActivity에 배경 저장/적용 헬퍼 추가 및 기본 프로필 적용 로직 구현

app/src/main/res/layout/fragment_chat_background_picker.xml

@@ -0,0 +1,50 @@
+<?xml version="1.0" encoding="utf-8"?>
+<androidx.constraintlayout.widget.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
+    xmlns:app="http://schemas.android.com/apk/res-auto"
+    android:layout_width="match_parent"
+    android:layout_height="match_parent"
+    android:background="@color/color_131313">
+
+    <LinearLayout
+        android:id="@+id/toolbar"
+        android:layout_width="0dp"
+        android:layout_height="56dp"
+        android:gravity="center_vertical"
+        android:orientation="horizontal"
+        android:paddingHorizontal="16dp"
+        app:layout_constraintEnd_toEndOf="parent"
+        app:layout_constraintStart_toStartOf="parent"
+        app:layout_constraintTop_toTopOf="parent">
+
+        <ImageView
+            android:id="@+id/iv_close"
+            android:layout_width="24dp"
+            android:layout_height="24dp"
+            android:contentDescription="닫기"
+            android:src="@drawable/ic_back" />
+
+        <TextView
+            android:id="@+id/tv_title"
+            android:layout_width="0dp"
+            android:layout_height="wrap_content"
+            android:layout_marginStart="12dp"
+            android:layout_weight="1"
+            android:ellipsize="end"
+            android:fontFamily="@font/pretendard_bold"
+            android:maxLines="1"
+            android:text="배경 사진 선택"
+            android:textColor="#FFFFFFFF"
+            android:textSize="20sp" />
+    </LinearLayout>
+
+    <androidx.recyclerview.widget.RecyclerView
+        android:id="@+id/rv_grid"
+        android:layout_width="0dp"
+        android:layout_height="0dp"
+        android:clipToPadding="false"
+        app:layout_constraintBottom_toBottomOf="parent"
+        app:layout_constraintEnd_toEndOf="parent"
+        app:layout_constraintStart_toStartOf="parent"
+        app:layout_constraintTop_toBottomOf="@id/toolbar" />
+
+</androidx.constraintlayout.widget.ConstraintLayout>