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/en.ts

@@ -1920,6 +1920,9 @@ export const dict = {
   'chat.chatInput.previewContextRemove': 'Remove preview context',
   'chat.chatInput.projectRoot': 'Project root',
   'chat.chatInput.branch': 'Branch',
+  'chat.chatInput.draftPicker.projectTitle': 'Project',
+  'chat.chatInput.draftPicker.searchProjects': 'Search projects...',
+  'chat.chatInput.draftPicker.searchBranches': 'Search branches...',
   'chat.chatInput.worktrees': 'Worktrees',
   'chat.chatInput.worktreeNew': '+ New',
   'chat.chatInput.drop.insertMention': 'Drop to insert as mention',

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

@@ -1886,6 +1886,9 @@ export const dict: Record<I18nKey, string> = {
   "chat.chatInput.previewContextRemove": "Quitar contexto de vista previa",
   "chat.chatInput.projectRoot": "Raíz del proyecto",
   "chat.chatInput.branch": "Rama",
+  "chat.chatInput.draftPicker.projectTitle": "Proyecto",
+  "chat.chatInput.draftPicker.searchProjects": "Buscar proyectos...",
+  "chat.chatInput.draftPicker.searchBranches": "Buscar ramas...",
   "chat.chatInput.worktrees": "Worktrees",
   "chat.chatInput.worktreeNew": "+ Nuevo",
   "chat.chatInput.drop.insertMention": "Suelta para insertar como mención",

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

@@ -1708,6 +1708,9 @@ export const dict = {
   'chat.chatInput.previewContextRemove': 'Supprimer le contexte d\'aperçu',
   'chat.chatInput.projectRoot': 'Racine du projet',
   'chat.chatInput.branch': 'Bifurquer',
+  'chat.chatInput.draftPicker.projectTitle': 'Projet',
+  'chat.chatInput.draftPicker.searchProjects': 'Rechercher des projets...',
+  'chat.chatInput.draftPicker.searchBranches': 'Rechercher des branches...',
   'chat.chatInput.worktrees': 'Worktrees',
   'chat.chatInput.worktreeNew': '+ Nouveau',
   'chat.chatInput.drop.insertMention': 'Déposer pour insérer comme mention',

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',

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

@@ -1920,6 +1920,9 @@ export const dict: Record<I18nKey, string> = {
   'chat.chatInput.previewContextRemove': '미리보기 컨텍스트 제거',
   'chat.chatInput.projectRoot': '프로젝트 루트',
   'chat.chatInput.branch': '브랜치',
+  'chat.chatInput.draftPicker.projectTitle': '프로젝트',
+  'chat.chatInput.draftPicker.searchProjects': '프로젝트 검색...',
+  'chat.chatInput.draftPicker.searchBranches': '브랜치 검색...',
   'chat.chatInput.worktrees': '워크트리',
   'chat.chatInput.worktreeNew': '+ 새로 만들기',
   'chat.chatInput.drop.insertMention': '여기에 놓아 멘션으로 추가',

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

@@ -1070,6 +1070,9 @@ export const dict: Record<I18nKey, string> = {
   'chat.chatInput.actions.sendMessageAria': 'Send message',
   'chat.chatInput.actions.stopGeneratingAria': 'Stop generating',
   'chat.chatInput.branch': 'Gałąź',
+  'chat.chatInput.draftPicker.projectTitle': 'Projekt',
+  'chat.chatInput.draftPicker.searchProjects': 'Szukaj projektów...',
+  'chat.chatInput.draftPicker.searchBranches': 'Szukaj gałęzi...',
   'chat.chatInput.devServerLogs': 'Dev Server logs:',
   'chat.chatInput.devServerLogsRemove': 'Usuń logi serwera deweloperskiego',
   'chat.chatInput.drop.attachFiles': 'Drop files here to attach',

packages/ui/src/lib/i18n/messages/pt-BR.ts

@@ -1886,6 +1886,9 @@ export const dict: Record<I18nKey, string> = {
   "chat.chatInput.previewContextRemove": "Remover contexto da visualização",
   "chat.chatInput.projectRoot": "Raiz do projeto",
   "chat.chatInput.branch": "Branch",
+  "chat.chatInput.draftPicker.projectTitle": "Projeto",
+  "chat.chatInput.draftPicker.searchProjects": "Buscar projetos...",
+  "chat.chatInput.draftPicker.searchBranches": "Buscar branches...",
   "chat.chatInput.worktrees": "Worktrees",
   "chat.chatInput.worktreeNew": "+ Novo",
   "chat.chatInput.drop.insertMention": "Solte para inserir como menção",

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

@@ -1886,6 +1886,9 @@ export const dict: Record<I18nKey, string> = {
   "chat.chatInput.previewContextRemove": "Прибрати контекст перегляду",
   "chat.chatInput.projectRoot": "Корінь проєкту",
   "chat.chatInput.branch": "гілка",
+  "chat.chatInput.draftPicker.projectTitle": "Проєкт",
+  "chat.chatInput.draftPicker.searchProjects": "Пошук проєктів...",
+  "chat.chatInput.draftPicker.searchBranches": "Пошук гілок...",
   "chat.chatInput.worktrees": "Worktree",
   "chat.chatInput.worktreeNew": "+ Новий",
   "chat.chatInput.drop.insertMention": "Відпустіть, щоб вставити як згадку",

packages/ui/src/lib/i18n/messages/zh-CN.ts

@@ -1886,6 +1886,9 @@ export const dict: Record<I18nKey, string> = {
   'chat.chatInput.previewContextRemove': '移除预览上下文',
   'chat.chatInput.projectRoot': '项目根目录',
   'chat.chatInput.branch': '分支',
+  'chat.chatInput.draftPicker.projectTitle': '项目',
+  'chat.chatInput.draftPicker.searchProjects': '搜索项目...',
+  'chat.chatInput.draftPicker.searchBranches': '搜索分支...',
   'chat.chatInput.worktrees': '工作树',
   'chat.chatInput.worktreeNew': '+ 新建',
   'chat.chatInput.drop.insertMention': '释放以插入为提及',

packages/ui/src/lib/i18n/messages/zh-TW.ts

@@ -1890,6 +1890,9 @@ export const dict: Record<I18nKey, string> = {
   'chat.chatInput.previewContextRemove': '移除預覽上下文',
   'chat.chatInput.projectRoot': '專案根目錄',
   'chat.chatInput.branch': '分支',
+  'chat.chatInput.draftPicker.projectTitle': '專案',
+  'chat.chatInput.draftPicker.searchProjects': '搜尋專案...',
+  'chat.chatInput.draftPicker.searchBranches': '搜尋分支...',
   'chat.chatInput.worktrees': 'Worktree',
   'chat.chatInput.worktreeNew': '+ 新增',
   'chat.chatInput.drop.insertMention': '放開以插入為提及',