feat(home): 최근 활동 이동 식별자를 보강한다

src/test/kotlin/kr/co/vividnext/sodalive/v2/api/home/HomeRecommendationControllerTest.kt

@@ -524,6 +524,28 @@ class HomeRecommendationControllerTest @Autowired constructor(
             .andExpect(jsonPath("$.data.items[0].creatorId").value(character.creatorMember!!.id))
     }
 
+    @Test
+    @DisplayName("최근 활동 라이브 크리에이터는 creatorId와 라이브 상태별 targetId를 노출한다")
+    fun shouldExposeNavigationIdsForRecentlyActiveLiveCreators() {
+        val activeCreator = saveMember("active-live-activity", MemberRole.CREATOR)
+        val inactiveCreator = saveMember("inactive-live-activity", MemberRole.CREATOR)
+        val baseAt = LocalDateTime.of(2026, 5, 31, 10, 0)
+        val activeLive = saveLiveRoom(activeCreator, baseAt.plusMinutes(2), "active-live-channel", isAdult = false)
+        saveLiveRoom(inactiveCreator, baseAt.plusMinutes(1), "inactive-live-channel", isAdult = false, isActive = false)
+        entityManager.flush()
+        entityManager.clear()
+
+        mockMvc.perform(get("/api/v2/home/recommendations"))
+            .andExpect(status().isOk)
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[0].creatorId").value(activeCreator.id))
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[0].activityType").value("LIVE"))
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[0].targetId").value(activeLive.id))
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[1].creatorId").value(inactiveCreator.id))
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[1].activityType").value("LIVE"))
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[1].targetId").hasJsonPath())
+            .andExpect(jsonPath("$.data.recentlyActiveCreators[1].targetId").doesNotExist())
+    }
+
     private fun saveMember(seed: String, role: MemberRole): Member {
         return memberRepository.saveAndFlush(
             Member(
@@ -548,7 +570,8 @@ class HomeRecommendationControllerTest @Autowired constructor(
         creator: Member,
         beginDateTime: LocalDateTime,
         channelName: String,
-        isAdult: Boolean
+        isAdult: Boolean,
+        isActive: Boolean = true
     ): LiveRoom {
         val room = LiveRoom(
             title = "live-${creator.nickname}-$channelName",
@@ -559,6 +582,7 @@ class HomeRecommendationControllerTest @Autowired constructor(
         )
         room.member = creator
         room.channelName = channelName
+        room.isActive = isActive
         entityManager.persist(room)
         return room
     }