feat(effects-02): route Action.Quit through sub-reducers; Effect.Quit last

Effect.Quit is appended at the tail of the effect list rather than
prepended, so all sub-reducer cleanup effects dispatch before runner
teardown. Combined with the sequential dispatch from effects-01, list
position is a runtime guarantee.

Closes finding #9.

apps/tui/src/main/kotlin/com/correx/apps/tui/reducer/RootReducer.kt

@@ -42,7 +42,9 @@ object RootReducer {
         clock: () -> Long,
     ): Pair<TuiState, List<Effect>> {
         log.debug("action={}", action::class.simpleName)
-        val quitEffects: List<Effect> = if (action is Action.Quit) listOf(Effect.Quit) else emptyList()
+        // Effect.Quit appended LAST so all cleanup effects from sub-reducers dispatch first.
+        // See effects-01 (sequential dispatch) for why list position is a runtime guarantee.
+        // I-Q3: sub-reducers must not synthesize Effect.Quit — it is a terminal signal owned by RootReducer.
         val prevInputMode = state.inputMode
         val prevInputBuffer = state.inputBuffer
 
@@ -78,6 +80,8 @@ object RootReducer {
 
             else -> withSubReducers
         }
-        return final to (quitEffects + ie + se + ce + pe)
+        val combined = ie + se + ce + pe
+        val withTerminal = if (action is Action.Quit) combined + Effect.Quit else combined
+        return final to withTerminal
     }
 }

apps/tui/src/test/kotlin/com/correx/apps/tui/reducer/RootReducerQuitTest.kt

@@ -0,0 +1,37 @@
+package com.correx.apps.tui.reducer
+
+import com.correx.apps.tui.input.Action
+import com.correx.apps.tui.state.TuiState
+import org.junit.jupiter.api.Assertions.assertEquals
+import org.junit.jupiter.api.Assertions.assertFalse
+import org.junit.jupiter.api.Assertions.assertTrue
+import org.junit.jupiter.api.Test
+
+class RootReducerQuitTest {
+
+    private val fixedClock: () -> Long = { 1000L }
+
+    @Test
+    fun `Effect Quit is the terminal effect when Action Quit is reduced`() {
+        val (_, effects) = RootReducer.reduce(TuiState(snapshotPhase = false), Action.Quit, fixedClock)
+        assertEquals(1, effects.count { it is Effect.Quit })
+        assertTrue(effects.last() is Effect.Quit)
+    }
+
+    @Test
+    fun `no Effect Quit when action is not Quit`() {
+        val (_, effects) = RootReducer.reduce(TuiState(snapshotPhase = false), Action.Connected, fixedClock)
+        assertFalse(effects.any { it is Effect.Quit })
+    }
+
+    @Test
+    fun `sub-reducers are invoked for Action Quit`() {
+        val initial = TuiState(snapshotPhase = false)
+        val (state, _) = RootReducer.reduce(initial, Action.Quit, fixedClock)
+        // ConnectionReducer handles Action.Quit by keeping state; verify state went through sub-reducers
+        // (state is the result of all sub-reducers, not an early-exit)
+        assertEquals(initial.inputMode, state.inputMode)
+        assertEquals(initial.sessions, state.sessions)
+        assertEquals(initial.connection, state.connection)
+    }
+}

apps/tui/src/test/kotlin/com/correx/apps/tui/reducer/SessionsReducerTest.kt

@@ -1,8 +1,11 @@
 package com.correx.apps.tui.reducer
 
+import com.correx.apps.server.protocol.ApprovalDto
+import com.correx.apps.server.protocol.ClientMessage
 import com.correx.apps.server.protocol.PauseReason
 import com.correx.apps.server.protocol.RiskSummaryDto
 import com.correx.apps.server.protocol.ServerMessage
+import com.correx.apps.server.protocol.SessionStateDto
 import com.correx.apps.tui.input.Action
 import com.correx.apps.tui.state.InputMode
 import com.correx.apps.tui.state.SessionSummary
@@ -171,7 +174,7 @@ class SessionsReducerTest {
         val (_, effects) = reduce(sessions = s, action = Action.CancelSelectedSession)
         assertEquals(1, effects.size)
         val effect = effects[0] as Effect.SendWs
-        val msg = effect.message as com.correx.apps.server.protocol.ClientMessage.CancelSession
+        val msg = effect.message as ClientMessage.CancelSession
         assertEquals("s1", msg.sessionId.value)
     }
 
@@ -293,8 +296,8 @@ class SessionsReducerTest {
     fun `SessionSnapshot with pendingApprovals populates pendingApproval on summary`() {
         val msg = ServerMessage.SessionSnapshot(
             sessionId = SessionId("s1"),
-            state = com.correx.apps.server.protocol.SessionStateDto("PAUSED", null, null),
-            pendingApprovals = listOf(com.correx.apps.server.protocol.ApprovalDto(requestId = "r9", tier = "T2")),
+            state = SessionStateDto("PAUSED", null, null),
+            pendingApprovals = listOf(ApprovalDto(requestId = "r9", tier = "T2")),
             lastSequence = 1L,
             lastSessionSequence = 1L,
         )
@@ -307,7 +310,7 @@ class SessionsReducerTest {
     fun `SessionSnapshot without pendingApprovals leaves pendingApproval null`() {
         val msg = ServerMessage.SessionSnapshot(
             sessionId = SessionId("s1"),
-            state = com.correx.apps.server.protocol.SessionStateDto("ACTIVE", null, null),
+            state = SessionStateDto("ACTIVE", null, null),
             pendingApprovals = emptyList(),
             lastSequence = 1L,
             lastSessionSequence = 1L,