web: use last-seen-recently fallback in private chat status

docs/core-checklist-status.md

@@ -9,7 +9,7 @@ Legend:
 
 1. Account - `DONE` (email auth, JWT, refresh, logout, reset, sessions; web handles `/verify-email?token=...` links with auth-page feedback; integration tests cover resend-verification replacement, password-reset login flow, and `check-email` status transitions)
 2. User Profile - `DONE` (username, name, avatar, bio, update)
-3. User Status - `PARTIAL` (online/last seen/offline; web now formats `just now/today/yesterday/recently`, backend-side presence heuristics still limited)
+3. User Status - `PARTIAL` (online/last seen/offline; web now formats `just now/today/yesterday/recently` and uses Telegram-like fallback `last seen recently` when precise last-seen is unavailable; backend-side presence heuristics still limited)
 4. Contacts - `PARTIAL` (list/search/add/remove/block/unblock; `add by email` flow covered by integration tests including `success/not found/blocked conflict`; web now surfaces specific add-by-email errors (`not found` vs `blocked`); UX moved to menu; Contacts panel now includes inline `Block/Unblock` actions per user)
 5. Chat List - `DONE` (all/pinned/archive/sort/unread; saved-messages delete behavior covered: clear history without deleting chat; regression test covers `GET /chats/{saved_id}` detail response)
 6. Chat Types - `DONE` (private/group/channel)