refactor(tui-03): remove ConnectSession from SessionStarted, keep on SessionSnapshot

SessionSnapshot is the correct trigger for connectSession() — the client
has enough state to stream live events at that point. SessionStarted fires
pre-snapshot and no longer needs to emit ConnectSession.

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

@@ -16,10 +16,10 @@ object RootReducer {
         val phase = SnapshotPhaseReducer.process(state, action)
         var current = phase.state
         val allEffects = mutableListOf<Effect>()
-        val isReplay = action is Action.ServerEventReceived &&
+        val replayingBufferedEvents = action is Action.ServerEventReceived &&
             action.message is ServerMessage.SnapshotComplete
         for (a in phase.actionsToDispatch) {
-            if (isReplay) {
+            if (replayingBufferedEvents) {
                 val inner = SnapshotPhaseReducer.process(current, a)
                 current = inner.state
                 for (ia in inner.actionsToDispatch) {

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

@@ -337,7 +337,7 @@ object SessionsReducer {
         msg: ServerMessage.SessionStarted,
         clock: () -> Long,
         sessions: SessionsState,
-    ): Pair<SessionsState, List<Effect.ConnectSession>> {
+    ): Pair<SessionsState, List<Effect>> {
         val summary = SessionSummary(
             id = msg.sessionId.value,
             status = "ACTIVE",
@@ -348,8 +348,7 @@ object SessionsReducer {
             lastOutput = null,
         )
         val selected = sessions.selectedId ?: msg.sessionId.value
-        return sessions.copy(sessions = sessions.sessions + summary, selectedId = selected) to
-                listOf(Effect.ConnectSession(msg.sessionId))
+        return sessions.copy(sessions = sessions.sessions + summary, selectedId = selected) to emptyList()
     }
 
     private fun processInferenceCompletedMessage(

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

@@ -77,6 +77,7 @@ object SnapshotPhaseReducer {
         is ServerMessage.ToolFailed -> msg.sessionId.value
         is ServerMessage.ToolRejected -> msg.sessionId.value
         is ServerMessage.ApprovalRequired -> msg.sessionId.value
+        is ServerMessage.SessionSnapshot -> msg.sessionId.value
         else -> null
     }
 

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

@@ -118,6 +118,20 @@ class RootReducerTest {
         assertEquals(state.sessions.sessions, newState.sessions.sessions)
     }
 
+    @Test
+    fun `SnapshotComplete with empty pendingEvents flips phase and produces no sessions`() {
+        val initial = TuiState(snapshotPhase = true, pendingEvents = emptyList())
+        val (result, effects) = RootReducer.reduce(
+            initial,
+            Action.ServerEventReceived(com.correx.apps.server.protocol.ServerMessage.SnapshotComplete),
+            fixedClock,
+        )
+        assertEquals(false, result.snapshotPhase)
+        assertTrue(result.pendingEvents.isEmpty())
+        assertTrue(result.sessions.sessions.isEmpty())
+        assertTrue(effects.isEmpty())
+    }
+
     @Test
     fun `AppendChar followed by Backspace returns to original buffer`() {
         val initial = TuiState(inputMode = InputMode.ROUTER, inputBuffer = "ab")

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

@@ -96,8 +96,7 @@ class SessionsReducerTest {
         assertEquals(1, state.sessions.size)
         assertEquals("s1", state.sessions[0].id)
         assertEquals("s1", state.selectedId)
-        assertEquals(1, effects.size)
-        assertTrue(effects[0] is Effect.ConnectSession)
+        assertTrue(effects.isEmpty())
     }
 
     @Test