feat(mobile): list managed Chats in the sessions sheet

Chat sessions without a project were dropped from the mobile session tree
because no registered project owned their directory. The sheet now partitions
sessions like the desktop sidebar and shows Chats as a collapsible section above
the project tree, with the same rows, swipe actions and paging; search results
label them "Chats" instead of the raw directory name.

Claude-Session: https://claude.ai/code/session_017TK5JAYDfT3Fotc23UEg98

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

@@ -103,6 +103,7 @@ export const dict = {
   'mobile.sessions.section.worktrees': 'Worktrees',
   'mobile.sessions.section.otherProjects': 'Projekt wechseln',
   'mobile.sessions.section.projects': 'Projekte',
+  'mobile.sessions.section.chats': 'Chats',
   'mobile.sessions.empty.noProjectsTitle': 'Noch keine Projekte',
   'mobile.sessions.empty.noProjectsDescription': 'Füge ein Projekt hinzu, um mit deinem Code zu chatten.',
   'mobile.sessions.empty.noSessionsTitle': 'Noch keine Sitzungen',

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

@@ -130,6 +130,7 @@ export const dict = {
   'mobile.sessions.section.worktrees': 'Worktrees',
   'mobile.sessions.section.otherProjects': 'Switch project',
   'mobile.sessions.section.projects': 'Projects',
+  'mobile.sessions.section.chats': 'Chats',
   'mobile.sessions.empty.noProjectsTitle': 'No projects yet',
   'mobile.sessions.empty.noProjectsDescription': 'Add a project to start chatting with your code.',
   'mobile.sessions.empty.noSessionsTitle': 'No sessions yet',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   "mobile.sessions.section.worktrees": "Worktrees",
   "mobile.sessions.section.otherProjects": "Cambiar de proyecto",
   "mobile.sessions.section.projects": "Proyectos",
+  "mobile.sessions.section.chats": "Chats",
   "mobile.sessions.empty.noProjectsTitle": "Sin proyectos",
   "mobile.sessions.empty.noProjectsDescription": "Agrega un proyecto para empezar a chatear con tu código.",
   "mobile.sessions.empty.noSessionsTitle": "Sin sesiones",

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

@@ -2918,6 +2918,7 @@ export const dict = {
   'mobile.sessions.section.worktrees': 'Worktrees',
   'mobile.sessions.section.otherProjects': 'Changer de projet',
   'mobile.sessions.section.projects': 'Projets',
+  'mobile.sessions.section.chats': 'Discussions',
   'mobile.sessions.empty.noProjectsTitle': 'Aucun projet pour le moment',
   'mobile.sessions.empty.noProjectsDescription': 'Ajoutez un projet pour commencer à discuter avec votre code.',
   'mobile.sessions.empty.noSessionsTitle': 'Aucune session pour le moment',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   'mobile.sessions.section.worktrees': 'ワークツリー',
   'mobile.sessions.section.otherProjects': 'プロジェクトを切り替え',
   'mobile.sessions.section.projects': 'プロジェクト',
+  'mobile.sessions.section.chats': 'チャット',
   'mobile.sessions.empty.noProjectsTitle': 'まだプロジェクトがありません',
   'mobile.sessions.empty.noProjectsDescription': 'プロジェクトを追加してコードとチャットを始めましょう。',
   'mobile.sessions.empty.noSessionsTitle': 'まだセッションがありません',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   'mobile.sessions.section.worktrees': '워크트리',
   'mobile.sessions.section.otherProjects': '프로젝트 전환',
   'mobile.sessions.section.projects': '프로젝트',
+  'mobile.sessions.section.chats': '채팅',
   'mobile.sessions.empty.noProjectsTitle': '프로젝트 없음',
   'mobile.sessions.empty.noProjectsDescription': '코드와 채팅을 시작하려면 프로젝트를 추가하세요.',
   'mobile.sessions.empty.noSessionsTitle': '세션 없음',

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

@@ -132,6 +132,7 @@ export const dict: Record<I18nKey, string> = {
   'mobile.sessions.section.worktrees': 'Worktrees',
   'mobile.sessions.section.otherProjects': 'Zmień projekt',
   'mobile.sessions.section.projects': 'Projekty',
+  'mobile.sessions.section.chats': 'Czaty',
   'mobile.sessions.empty.noProjectsTitle': 'Brak projektów',
   'mobile.sessions.empty.noProjectsDescription': 'Dodaj projekt, aby zacząć rozmawiać ze swoim kodem.',
   'mobile.sessions.empty.noSessionsTitle': 'Brak sesji',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   "mobile.sessions.section.worktrees": "Worktrees",
   "mobile.sessions.section.otherProjects": "Trocar de projeto",
   "mobile.sessions.section.projects": "Projetos",
+  "mobile.sessions.section.chats": "Conversas",
   "mobile.sessions.empty.noProjectsTitle": "Sem projetos",
   "mobile.sessions.empty.noProjectsDescription": "Adicione um projeto para começar a conversar com seu código.",
   "mobile.sessions.empty.noSessionsTitle": "Sem sessões",

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

@@ -117,6 +117,7 @@ export const dict = {
   'mobile.sessions.section.worktrees': 'Worktree\'ler',
   'mobile.sessions.section.otherProjects': 'Proje değiştir',
   'mobile.sessions.section.projects': 'Projeler',
+  'mobile.sessions.section.chats': 'Sohbetler',
   'mobile.sessions.empty.noProjectsTitle': 'Henüz proje yok',
   'mobile.sessions.empty.noProjectsDescription': 'Kodunuzla sohbet etmeye başlamak için bir proje ekleyin.',
   'mobile.sessions.empty.noSessionsTitle': 'Henüz session yok',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   "mobile.sessions.section.worktrees": "Worktrees",
   "mobile.sessions.section.otherProjects": "Інші проєкти",
   "mobile.sessions.section.projects": "Проєкти",
+  "mobile.sessions.section.chats": "Чати",
   "mobile.sessions.empty.noProjectsTitle": "Ще немає проєктів",
   "mobile.sessions.empty.noProjectsDescription": "Додай проєкт, щоб почати спілкування з кодом.",
   "mobile.sessions.empty.noSessionsTitle": "Ще немає сесій",

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   'mobile.sessions.section.worktrees': '工作树',
   'mobile.sessions.section.otherProjects': '切换项目',
   'mobile.sessions.section.projects': '项目',
+  'mobile.sessions.section.chats': '聊天',
   'mobile.sessions.empty.noProjectsTitle': '暂无项目',
   'mobile.sessions.empty.noProjectsDescription': '添加项目以开始与代码对话。',
   'mobile.sessions.empty.noSessionsTitle': '暂无会话',

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

@@ -131,6 +131,7 @@ export const dict: Record<I18nKey, string> = {
   'mobile.sessions.section.worktrees': '工作樹',
   'mobile.sessions.section.otherProjects': '切換專案',
   'mobile.sessions.section.projects': '專案',
+  'mobile.sessions.section.chats': '聊天',
   'mobile.sessions.empty.noProjectsTitle': '尚無專案',
   'mobile.sessions.empty.noProjectsDescription': '新增專案即可開始與程式碼聊天。',
   'mobile.sessions.empty.noSessionsTitle': '尚無會話',