feat(chat): direct chats and groups between users in the pet's window

Server mode: a rail beside the pet's chat lists the pet, then the user's
direct chats (one per pair) and groups with unread counts, and + for a new
chat. A room shows its messages (group senders named), loads older pages,
and sends text, pasted / dropped / attached files (<= 10 x 25 MB; images
inline). A group's creator renames it and adds or removes people; anyone may
leave. A blue dot on the pet counts unread messages.

Only a room's members read or write it, an admin included (roomFor → 404).
Files are stored under server-made names in <data dir>/chat/<room>/ and
served to members only under a sandbox CSP + nosniff. chat_message /
chat_room frames reach exactly the ids in `to` (scope.exactAudience).
New tables chat_rooms / chat_members / chat_messages / chat_files (additive).

client/src/components/Sagi/sagi.css

@@ -6,7 +6,8 @@
  * infinite animation makes the browser draw a new frame 60 times a second for
  * as long as the page is open (the drop-shadow filter re-rendered each time),
  * which made the whole desktop stutter. All motion is disabled under
- * [data-reduced="1"] and prefers-reduced-motion.
+ * [data-reduced="1"] and prefers-reduced-motion. The blue dot counts unread
+ * chat messages from other users (server mode).
  * Transform origins are the delicate part - see the comments on .sagi-avatar
  * and .sagi-eye-blink for which reference box each one resolves against.
  * @author Nguyễn Ngọc Trí Vĩ <vinnt@smartgift.vn>
@@ -406,6 +407,25 @@
   outline: 2px solid #818cf8;
   outline-offset: 3px;
 }
+/* Unread chat messages from other users: top-left, opposite the error dot. */
+.sagi-chat-dot {
+  position: absolute;
+  top: 2px;
+  left: 2px;
+  min-width: 14px;
+  height: 14px;
+  padding: 0 2px;
+  border-radius: 9999px;
+  background: #3b82f6;
+  color: #fff;
+  font-size: 9px;
+  font-weight: 700;
+  display: flex;
+  align-items: center;
+  justify-content: center;
+  border: 2px solid #0c0c14;
+}
+
 .sagi-error-dot {
   position: absolute;
   top: 2px;