feat(cli): show session/conversation ID in footer

Adds a third line to the footer, right-aligned beneath Gateway status:
'session: a1b2c3d4' (first 8 chars) or 'no session' when not connected.

packages/cli/src/tui/app.tsx

@@ -77,6 +77,7 @@ export function TuiApp({ gatewayUrl, conversationId, sessionCookie }: TuiAppProp
         modelName={socket.modelName}
         providerName={socket.providerName}
         thinkingLevel={socket.thinkingLevel}
+        conversationId={socket.conversationId}
       />
     </Box>
   );

packages/cli/src/tui/components/bottom-bar.tsx

@@ -11,6 +11,7 @@ export interface BottomBarProps {
   modelName: string | null;
   providerName: string | null;
   thinkingLevel: string;
+  conversationId: string | undefined;
 }
 
 function formatTokens(n: number): string {
@@ -36,6 +37,7 @@ export function BottomBar({
   modelName,
   providerName,
   thinkingLevel,
+  conversationId,
 }: BottomBarProps) {
   const gatewayStatus = connected ? 'Connected' : connecting ? 'Connecting…' : 'Disconnected';
   const gatewayColor = connected ? 'green' : connecting ? 'yellow' : 'red';
@@ -56,7 +58,17 @@ export function BottomBar({
         </Box>
       </Box>
 
-      {/* Line 2: token stats  ·····  (provider) model */}
+      {/* Line 2: token stats  ·····  session id */}
+      <Box justifyContent="space-between">
+        <Box />
+        <Box>
+          <Text dimColor>
+            {conversationId ? `session: ${conversationId.slice(0, 8)}` : 'no session'}
+          </Text>
+        </Box>
+      </Box>
+
+      {/* Line 3: token stats  ·····  (provider) model */}
       <Box justifyContent="space-between" minHeight={1}>
         <Box>
           {hasTokens ? (