fix(home): 최근 활동 라이브 활성 필터를 제거한다

src/main/kotlin/kr/co/vividnext/sodalive/v2/recommendation/adapter/out/persistence/DefaultHomeRecommendationQueryRepository.kt

@@ -148,8 +148,7 @@ class DefaultHomeRecommendationQueryRepository(
                            lr.id as target_sort_id
                     from live_room lr
                     join member m on m.id = lr.member_id
-                    where lr.is_active = true
-                      and lr.channel_name is not null
+                    where lr.channel_name is not null
                       and lr.channel_name <> ''
                       and (:includeAdultActivities = true or lr.is_adult = false)
                       and m.is_active = true

src/test/kotlin/kr/co/vividnext/sodalive/v2/recommendation/adapter/out/persistence/DefaultHomeRecommendationQueryRepositoryTest.kt

@@ -437,6 +437,31 @@ class DefaultHomeRecommendationQueryRepositoryTest @Autowired constructor(
         assertEquals(communityCreator.id, byCreatorNickname[communityCreator.nickname]!!.targetId)
     }
 
+    @Test
+    @DisplayName("최근 활동 크리에이터는 라이브 활성 여부와 무관하게 채널명이 있는 라이브를 포함한다")
+    fun shouldIncludeInactiveLiveWithChannelNameInRecentlyActiveCreators() {
+        val baseAt = LocalDateTime.of(2026, 5, 31, 10, 0)
+        val inactiveLiveCreator = saveMember("activity-inactive-live", MemberRole.CREATOR)
+        val blankChannelCreator = saveMember("activity-blank-channel", MemberRole.CREATOR)
+        val emptyChannelCreator = saveMember("activity-empty-channel", MemberRole.CREATOR)
+        saveLiveRoom(
+            inactiveLiveCreator,
+            baseAt.plusMinutes(2),
+            channelName = "inactive-live-channel",
+            isActive = false
+        )
+        saveLiveRoom(blankChannelCreator, baseAt.plusMinutes(1), channelName = null, isActive = false)
+        saveLiveRoom(emptyChannelCreator, baseAt, channelName = "", isActive = false)
+        flushAndClear()
+
+        val creators = repository.findRecentlyActiveCreators(limit = 10)
+
+        assertEquals(listOf(inactiveLiveCreator.nickname), creators.map { it.creatorNickname })
+        assertEquals(CreatorActivityType.LIVE, creators.single().activityType)
+        assertEquals(baseAt.plusMinutes(2), creators.single().activityAt)
+        assertEquals(null, creators.single().targetId)
+    }
+
     @Test
     @DisplayName("최근 활동 크리에이터는 성인 노출 정책이 꺼져 있으면 성인 라이브/오디오/커뮤니티 활동을 제외한다")
     fun shouldExcludeAdultActivitiesFromRecentlyActiveCreatorsWhenAdultHidden() {