feat(chat): 내 채팅방 목록 페이징 적용 및 page 파라미터 추가

- Repository에 Pageable 인자로 전달하여 DB 레벨 limit/offset 적용
- Service에서 PageRequest.of(page, 20)로 20개 페이지 처리 고정
- Controller /api/chat/room/list에 page 요청 파라미터 추가 및 전달

왜: 참여 중인 채팅방 목록이 페이징되지 않아 20개 단위로 최신 메시지 기준 내림차순 페이징 처리 필요

src/main/kotlin/kr/co/vividnext/sodalive/chat/room/controller/ChatRoomController.kt

@@ -54,12 +54,13 @@ class ChatRoomController(
      */
     @GetMapping("/list")
     fun listMyChatRooms(
-        @AuthenticationPrincipal(expression = "#this == 'anonymousUser' ? null : member") member: Member?
+        @AuthenticationPrincipal(expression = "#this == 'anonymousUser' ? null : member") member: Member?,
+        @RequestParam(defaultValue = "0") page: Int
     ) = run {
         if (member == null || member.auth == null) {
             ApiResponse.ok(emptyList())
         } else {
-            val response = chatRoomService.listMyChatRooms(member)
+            val response = chatRoomService.listMyChatRooms(member, page)
             ApiResponse.ok(response)
         }
     }

src/main/kotlin/kr/co/vividnext/sodalive/chat/room/repository/ChatRoomRepository.kt

@@ -4,6 +4,7 @@ import kr.co.vividnext.sodalive.chat.character.ChatCharacter
 import kr.co.vividnext.sodalive.chat.room.ChatRoom
 import kr.co.vividnext.sodalive.chat.room.dto.ChatRoomListQueryDto
 import kr.co.vividnext.sodalive.member.Member
+import org.springframework.data.domain.Pageable
 import org.springframework.data.jpa.repository.JpaRepository
 import org.springframework.data.jpa.repository.Query
 import org.springframework.data.repository.query.Param
@@ -55,6 +56,7 @@ interface ChatRoomRepository : JpaRepository<ChatRoom, Long> {
         """
     )
     fun findMemberRoomsOrderByLastMessageDesc(
-        @Param("member") member: Member
+        @Param("member") member: Member,
+        pageable: Pageable
     ): List<ChatRoomListQueryDto>
 }

src/main/kotlin/kr/co/vividnext/sodalive/chat/room/service/ChatRoomService.kt

@@ -21,6 +21,7 @@ import kr.co.vividnext.sodalive.common.SodaException
 import kr.co.vividnext.sodalive.member.Member
 import org.slf4j.LoggerFactory
 import org.springframework.beans.factory.annotation.Value
+import org.springframework.data.domain.PageRequest
 import org.springframework.http.HttpEntity
 import org.springframework.http.HttpHeaders
 import org.springframework.http.HttpMethod
@@ -183,8 +184,13 @@ class ChatRoomService(
     }
 
     @Transactional(readOnly = true)
-    fun listMyChatRooms(member: Member): List<ChatRoomListItemDto> {
-        val rooms: List<ChatRoomListQueryDto> = chatRoomRepository.findMemberRoomsOrderByLastMessageDesc(member)
+    fun listMyChatRooms(member: Member, page: Int): List<ChatRoomListItemDto> {
+        // 기본 페이지당 20개 고정
+        val pageable = PageRequest.of(if (page < 0) 0 else page, 20)
+        val rooms: List<ChatRoomListQueryDto> = chatRoomRepository.findMemberRoomsOrderByLastMessageDesc(
+            member,
+            pageable
+        )
         return rooms.map { q ->
             val room = ChatRoom(
                 sessionId = "",