feat(status): improve last-seen labels in web private chats

docs/core-checklist-status.md

@@ -9,7 +9,7 @@ Legend:
 
 1. Account - `PARTIAL` (email auth, JWT, refresh, logout, reset; sessions exist, full UX still improving)
 2. User Profile - `DONE` (username, name, avatar, bio, update)
-3. User Status - `PARTIAL` (online/last seen/offline; "recently" heuristic limited)
+3. User Status - `PARTIAL` (online/last seen/offline; web now formats `just now/today/yesterday/recently`, 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`; UX moved to menu)
 5. Chat List - `DONE` (all/pinned/archive/sort/unread; saved-messages delete behavior covered: clear history without deleting chat)
 6. Chat Types - `DONE` (private/group/channel)

web/src/components/ChatInfoPanel.tsx

@@ -878,6 +878,26 @@ function formatLastSeen(value: string): string {
   if (Number.isNaN(date.getTime())) {
     return "recently";
   }
+  const now = new Date();
+  const diffMs = now.getTime() - date.getTime();
+  if (diffMs < 0) {
+    return "recently";
+  }
+  const minute = 60 * 1000;
+  const hour = 60 * minute;
+  const day = 24 * hour;
+  if (diffMs < 2 * minute) {
+    return "just now";
+  }
+  if (diffMs < day) {
+    return `today at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 2 * day) {
+    return `yesterday at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 7 * day) {
+    return "recently";
+  }
   return date.toLocaleString(undefined, {
     day: "2-digit",
     month: "short",

web/src/components/ChatList.tsx

@@ -895,6 +895,26 @@ function formatLastSeen(value: string): string {
   if (Number.isNaN(date.getTime())) {
     return "recently";
   }
+  const now = new Date();
+  const diffMs = now.getTime() - date.getTime();
+  if (diffMs < 0) {
+    return "recently";
+  }
+  const minute = 60 * 1000;
+  const hour = 60 * minute;
+  const day = 24 * hour;
+  if (diffMs < 2 * minute) {
+    return "just now";
+  }
+  if (diffMs < day) {
+    return `today at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 2 * day) {
+    return `yesterday at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 7 * day) {
+    return "recently";
+  }
   return date.toLocaleString(undefined, {
     day: "2-digit",
     month: "short",

web/src/pages/ChatsPage.tsx

@@ -317,6 +317,26 @@ function formatLastSeen(value: string): string {
   if (Number.isNaN(date.getTime())) {
     return "recently";
   }
+  const now = new Date();
+  const diffMs = now.getTime() - date.getTime();
+  if (diffMs < 0) {
+    return "recently";
+  }
+  const minute = 60 * 1000;
+  const hour = 60 * minute;
+  const day = 24 * hour;
+  if (diffMs < 2 * minute) {
+    return "just now";
+  }
+  if (diffMs < day) {
+    return `today at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 2 * day) {
+    return `yesterday at ${date.toLocaleTimeString([], { hour: "2-digit", minute: "2-digit" })}`;
+  }
+  if (diffMs < 7 * day) {
+    return "recently";
+  }
   return date.toLocaleString(undefined, {
     day: "2-digit",
     month: "short",