feat(mobile): collapsed pill composer and mobile input redesign

Mobile composer redesign: when the keyboard is closed the input collapses
into a narrow pill (sessions, attach, placeholder, mic) with a round
new-session button that fades away on the draft screen. Model and agent
selectors move into a row above the textarea; the draft project/branch
pickers and the attachment menu become searchable bottom sheets reusing
MobileOverlayPanel; a drag handle (also available while dictating) swipes
the composer into and out of a fullscreen mode.

Keyboard-lifecycle hardening: composer controls (agent cycle, dictation
and its overlay controls) no longer steal focus and dismiss the keyboard;
overlays reopen the keyboard on close via a debounced restore chain that
survives menu-to-picker handoffs and skips the native file picker; open
overlays and dictation keep the composer expanded. Dictation starts
directly from the pill and its overlay content fades in after the shape
settles. The keyboard slide compensates the pill-to-full height change in
one motion, and the mobile highlight mirror is disabled so the caret
always matches the text layout.

packages/ui/src/lib/i18n/messages/ja.ts

@@ -1919,6 +1919,9 @@ export const dict: Record<I18nKey, string> = {
   'chat.chatInput.previewContextRemove': 'プレビューコンテキストを削除',
   'chat.chatInput.projectRoot': 'プロジェクトルート',
   'chat.chatInput.branch': 'ブランチ',
+  'chat.chatInput.draftPicker.projectTitle': 'プロジェクト',
+  'chat.chatInput.draftPicker.searchProjects': 'プロジェクトを検索...',
+  'chat.chatInput.draftPicker.searchBranches': 'ブランチを検索...',
   'chat.chatInput.worktrees': 'ワークツリー',
   'chat.chatInput.worktreeNew': '+ 新規',
   'chat.chatInput.drop.insertMention': 'ドロップしてメンションとして挿入',