feat(ios): P1-B — W7 UI wave: deep links, timeline, quick-reply, diff, projects, session switcher, thumbnails, lock-screen push

T-iOS-22: DeepLinkRouter (full-field whitelist, cold-start stash, route(from:) for push-tap reuse), 21 tests
T-iOS-24: TimelineSheet mirroring web render() order; disabled→empty-state; reuses AwayDigest onExpand
T-iOS-25: QuickReply chips (built-ins mirror quick-reply.ts via KeyByteMap; visible iff live gate && !readOnly)
T-iOS-27: read-only DiffScreen + App-layer DiffFetcher (RO no-Origin; APIClient fold-in noted for T-iOS-38 owner)
T-iOS-26: Projects list/detail — grouping byte-identical to web group keys (prefs-shared collapse state),
prefs-clobber defenses (no blind PUT on empty base; adopt server echo), claude\r bootstrap
T-iOS-23: UnreadLedger + TitleSanitizer (SessionCore, +15 tests), lastOutputAt decode, list-boundary re-sanitize
T-iOS-29: new-in-cwd (untrusted cwd, no bootstrap re-injection) + exited-session reopen; fixes stale-controller
SwiftTerm view bug via .id(controller.id)
T-iOS-28: offscreen SwiftTerm thumbnail pipeline (LRU 32, concurrency gate 2, 256KiB cap, grid clamp)
T-iOS-21: PushRegistrar (WEBTERM_GATE category: Allow=.authenticationRequired, no .foreground) +
NotificationActionHandler (whitelisted payload, token never persisted, bg-task-wrapped POST, 403 fallback)
CRITICAL fix (verify-found boot crash): @Sendable literals on UN completion closures — MainActor-inherited
closures trapped Swift 6 executor check on UN's background queue; boot re-verified (no new crash reports,
permission prompt reached, privacy shade correctly covering during system alert)
Verified: 261 pkg + 247 app + 10 integration tests green; 7/7 semantics checks; Owns audit clean

ios/Packages/APIClient/Sources/APIClient/Models.swift

@@ -28,6 +28,10 @@ public struct LiveSessionInfo: Sendable, Equatable {
     public let rows: Int
     /// Latest statusLine telemetry, if any (B2).
     public let telemetry: StatusTelemetry?
+    /// Server ms timestamp of the last PTY output (== createdAt until first
+    /// output). OPTIONAL additive field (T-iOS-37, src/types.ts:259-261) —
+    /// pre-P1 servers omit it; nil means "no unread data source" (T-iOS-23).
+    public let lastOutputAt: Int?
 
     public init(
         id: UUID,
@@ -38,7 +42,8 @@ public struct LiveSessionInfo: Sendable, Equatable {
         cwd: String?,
         cols: Int,
         rows: Int,
-        telemetry: StatusTelemetry?
+        telemetry: StatusTelemetry?,
+        lastOutputAt: Int? = nil
     ) {
         self.id = id
         self.createdAt = createdAt
@@ -49,12 +54,14 @@ public struct LiveSessionInfo: Sendable, Equatable {
         self.cols = cols
         self.rows = rows
         self.telemetry = telemetry
+        self.lastOutputAt = lastOutputAt
     }
 }
 
 extension LiveSessionInfo: Decodable {
     private enum CodingKeys: String, CodingKey {
         case id, createdAt, clientCount, status, exited, cwd, cols, rows, telemetry
+        case lastOutputAt
     }
 
     public init(from decoder: any Decoder) throws {
@@ -71,6 +78,7 @@ extension LiveSessionInfo: Decodable {
         // Optional/nullable fields: wrong type degrades to nil (tolerant).
         cwd = try? container.decode(String.self, forKey: .cwd)
         telemetry = try? container.decode(StatusTelemetry.self, forKey: .telemetry)
+        lastOutputAt = try? container.decode(Int.self, forKey: .lastOutputAt)
     }
 
     /// Decode a `/live-sessions` response body.