Push the whole composer up with the keyboard on mobile

The keyboard shift was applied only to the input box inside the
composer, so the subagents track and the draft import-session pill —
rendered as siblings above the composer — stayed behind the keyboard.
Lift the shift to the wrapper that holds the full composer column and
add an opt-out prop so the composer skips its own shift when a parent
owns it.

packages/app/src/composer/draft/workspace-tab.tsx

@@ -1,7 +1,9 @@
 import { useCallback, useEffect, useMemo, useRef } from "react";
 import { Keyboard, ScrollView, Text, View } from "react-native";
+import ReanimatedAnimated from "react-native-reanimated";
 import { StyleSheet } from "react-native-unistyles";
 import { useSafeAreaInsets } from "react-native-safe-area-context";
+import { useKeyboardShiftStyle } from "@/hooks/use-keyboard-shift-style";
 import invariant from "tiny-invariant";
 import { Composer } from "@/composer";
 import { DraftAgentModeControl } from "@/composer/agent-controls/mode-control";
@@ -584,9 +586,13 @@ export function WorkspaceDraftAgentTab({
     [composerState],
   );
 
+  const { style: composerKeyboardStyle } = useKeyboardShiftStyle({
+    mode: "translate",
+  });
+
   const inputAreaWrapperStyle = useMemo(
-    () => [styles.inputAreaWrapper, { paddingBottom: insets.bottom }],
-    [insets.bottom],
+    () => [styles.inputAreaWrapper, { paddingBottom: insets.bottom }, composerKeyboardStyle],
+    [insets.bottom, composerKeyboardStyle],
   );
 
   const handleDropdownCloseFocus = useCallback(() => {
@@ -656,7 +662,7 @@ export function WorkspaceDraftAgentTab({
           )}
         </View>
 
-        <View style={inputAreaWrapperStyle}>
+        <ReanimatedAnimated.View style={inputAreaWrapperStyle}>
           {importPillPress ? (
             <View style={styles.importPillRow}>
               <View style={styles.importPillContent}>
@@ -667,6 +673,7 @@ export function WorkspaceDraftAgentTab({
           <Composer
             agentId={tabId}
             serverId={serverId}
+            externalKeyboardShift
             isPaneFocused={isPaneFocused}
             onSubmitMessage={handleCreateFromInput}
             isSubmitLoading={isSubmitting}
@@ -686,7 +693,7 @@ export function WorkspaceDraftAgentTab({
             agentControls={composerAgentControls}
             footer={composerFooter}
           />
-        </View>
+        </ReanimatedAnimated.View>
       </View>
     </FileDropZone>
   );