feat: wire ChatMode.STEERING toggle in TUI input bar

- Add ChatMode.STEERING toggle via ctrl+s keybinding
- Add KeyEvent.ToggleSteeringMode, Action.CycleChatMode
- TambouiKeyMapper: map ctrl+s to ToggleSteeringMode
- KeyResolver: route ToggleSteeringMode to CycleChatMode (global)
- InputReducer: toggle chatMode between CHAT and STEERING
- TuiState: add chatMode field (default CHAT)
- SessionsReducer: use ctx.chatMode instead of hardcoded CHAT
- RootReducer: pass afterInput.chatMode to SessionsReducerContext
- InputBar: show blue 'chat' or magenta 'steer' label in status line

Activation: ctrl+s toggles mode, 'steer' label appears, submitted
ChatInput uses ChatMode.STEERING → router emits SteeringNoteAddedEvent
→ context builder folds into next stage's context pack

apps/tui/src/main/kotlin/com/correx/apps/tui/KeyEvent.kt

@@ -20,4 +20,5 @@ sealed class KeyEvent {
     object CursorLeft : KeyEvent()
     object CursorRight : KeyEvent()
     object ToggleWorkflows : KeyEvent()
+    object ToggleSteeringMode : KeyEvent()
 }

apps/tui/src/main/kotlin/com/correx/apps/tui/components/InputBar.kt

@@ -18,6 +18,11 @@ private fun promptStyle(inputMode: InputMode): Style = when (inputMode) {
     InputMode.FILTER -> Style.create().yellow()
 }
 
+private fun chatModeLabel(state: TuiState): Span = when (state.chatMode) {
+    com.correx.core.router.ChatMode.CHAT -> Span.styled("chat", Style.create().blue())
+    com.correx.core.router.ChatMode.STEERING -> Span.styled("steer", Style.create().magenta())
+}
+
 private fun cursorLine(buffer: String, cursor: Int, inputMode: InputMode): Line {
     val prompt = Span.styled("▌", promptStyle(inputMode))
     if (buffer.isEmpty()) return Line.from(prompt, Span.raw(""))
@@ -77,7 +82,9 @@ private fun createRowsForIdleRouter(
     }
     return row1 to Line.from(
         Span.styled(sessionName, Style.create().cyan()),
-        Span.styled(" · router  ", dimStyle),
+        Span.styled(" · ", dimStyle),
+        chatModeLabel(state),
+        Span.styled("  ", dimStyle),
         Span.styled("tab", Style.create().blue()),
         Span.styled(" filter  ", dimStyle),
         Span.styled("ctrl+n", Style.create().blue()),
@@ -101,7 +108,9 @@ private fun createRowsForInSessionRouter(
     }
     return row1 to Line.from(
         Span.styled(sessionName, Style.create().cyan()),
-        Span.styled(" · router  ", dimStyle),
+        Span.styled(" · ", dimStyle),
+        chatModeLabel(state),
+        Span.styled("  ", dimStyle),
         Span.styled("tab", Style.create().blue()),
         Span.styled(" filter  ", dimStyle),
         Span.styled("↑↓", Style.create().blue()),

apps/tui/src/main/kotlin/com/correx/apps/tui/input/Action.kt

@@ -27,5 +27,6 @@ sealed interface Action {
     data object CursorLeft : Action
     data object CursorRight : Action
     data object ToggleWorkflows : Action
+    data object CycleChatMode : Action
     data object NoOp : Action
 }

apps/tui/src/main/kotlin/com/correx/apps/tui/input/KeyResolver.kt

@@ -17,6 +17,7 @@ object KeyResolver {
             KeyEvent.Quit -> Action.Quit
             KeyEvent.Approve -> Action.ApproveActive
             KeyEvent.Reject -> Action.RejectActive
+            KeyEvent.ToggleSteeringMode -> Action.CycleChatMode
             else -> null
         }
         if (global != null) return global

apps/tui/src/main/kotlin/com/correx/apps/tui/input/TambouiKeyMapper.kt

@@ -24,6 +24,7 @@ fun mapKey(event: TambouiKeyEvent): KeyEvent? {
             event.isChar('e') -> KeyEvent.ToggleEventStrip
             event.isChar('h') -> KeyEvent.ShowPendingApproval
             event.isChar('w') -> KeyEvent.ToggleWorkflows
+            event.isChar('s') -> KeyEvent.ToggleSteeringMode
             else -> null
         }
     }

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

@@ -7,6 +7,7 @@ import com.correx.apps.tui.state.InputMode
 import com.correx.apps.tui.state.TuiState
 import com.correx.apps.tui.state.selectedPendingApproval
 import com.correx.core.events.types.ApprovalRequestId
+import com.correx.core.router.ChatMode
 
 object InputReducer {
     @Suppress("CyclomaticComplexMethod")
@@ -21,6 +22,13 @@ object InputReducer {
             },
         ) to emptyList()
 
+        is Action.CycleChatMode -> state.copy(
+            chatMode = when (state.chatMode) {
+                ChatMode.CHAT -> ChatMode.STEERING
+                ChatMode.STEERING -> ChatMode.CHAT
+            },
+        ) to emptyList()
+
         is Action.CursorLeft -> state.copy(
             inputCursor = (state.inputCursor - 1).coerceAtLeast(0),
         ) to emptyList()

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

@@ -69,6 +69,7 @@ object RootReducer {
                 inputText = prevInputBuffer,
                 action = action,
                 clock = clock,
+                chatMode = afterInput.chatMode,
             ),
         )
         log.debug("connection state before reducers={}", state.connection)

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

@@ -29,6 +29,7 @@ data class SessionsReducerContext(
     val inputText: String,
     val action: Action,
     val clock: () -> Long = System::currentTimeMillis,
+    val chatMode: ChatMode = ChatMode.CHAT,
 )
 
 object SessionsReducer {
@@ -89,7 +90,7 @@ object SessionsReducer {
                         ClientMessage.ChatInput(
                             sessionId = SessionId(sid),
                             text = ctx.inputText,
-                            mode = ChatMode.CHAT,
+                            mode = ctx.chatMode,
                         ),
                     ),
                 )

apps/tui/src/main/kotlin/com/correx/apps/tui/state/TuiState.kt

@@ -2,6 +2,7 @@ package com.correx.apps.tui.state
 
 import com.correx.apps.server.protocol.ApprovalDecision
 import com.correx.apps.server.protocol.ServerMessage
+import com.correx.core.router.ChatMode
 
 enum class InputMode { ROUTER, FILTER }
 
@@ -46,6 +47,7 @@ data class TuiState(
     val providerType: ProviderType = ProviderType.LOCAL,
     val routerConnected: Boolean = false,
     val routerMessages: Map<String, List<String>> = emptyMap(),
+    val chatMode: ChatMode = ChatMode.CHAT,
     /**
      * True from connect until SnapshotComplete observed. Reset to true on Disconnected.
      * When true, event-bearing messages are buffered in [pendingEvents]; snapshots are applied immediately.