feat: add TUI session orchestrator

Add a first-class active-session orchestrator for the Ink TUI:

- list, activate, close, and launch live process-local TUI sessions
- hydrate committed and in-flight output when switching sessions
- dispatch a new prompt session from the +new row with session-scoped model picks
- expose a clickable live-session count in the status chrome
- preserve stable row order while initially focusing the current session
- support mouse hit-testing for floating orchestrator overlays
- add backend and frontend regression coverage for the lifecycle and UI helpers

ui-tui/src/gatewayTypes.ts

@@ -122,6 +122,43 @@ export interface SessionResumeResponse {
   session_id: string
 }
 
+export type LiveSessionStatus = 'idle' | 'starting' | 'waiting' | 'working'
+
+export interface SessionActiveItem {
+  current?: boolean
+  id: string
+  last_active?: number
+  message_count?: number
+  model?: string
+  preview?: string
+  session_key?: string
+  started_at?: number
+  status: LiveSessionStatus
+  title?: string
+}
+
+export interface SessionActiveListResponse {
+  sessions?: SessionActiveItem[]
+}
+
+export interface SessionInflightTurn {
+  assistant?: string
+  streaming?: boolean
+  user?: string
+}
+
+export interface SessionActivateResponse {
+  inflight?: null | SessionInflightTurn
+  info?: SessionInfo
+  message_count?: number
+  messages: GatewayTranscriptMessage[]
+  running?: boolean
+  session_id: string
+  session_key?: string
+  started_at?: number
+  status?: LiveSessionStatus
+}
+
 export interface SessionListItem {
   id: string
   message_count: number
@@ -203,6 +240,7 @@ export interface SessionBranchResponse {
 }
 
 export interface SessionCloseResponse {
+  closed?: boolean
   ok?: boolean
 }