Add persistent agent messaging and shared chat bubbles

Connect Sybil to the Pi root conversation with authenticated REST and WebSocket
APIs, persistent read state, and a dedicated agent tab. Keep optimistic messages
stable through delivery and retries, and animate arrivals without losing the
reader's scroll position.

Share bubble styling with regular chats and remove the obsolete admission sender.
Reject malformed upstream receipts and WebSocket upgrade requests, with regression
coverage and updated API documentation.

Validated with 51 web tests, 44 server tests, both production builds, desktop/mobile
bubble comparisons, and 11 browser animation and scrolling checks.

server/prisma/schema.prisma

@@ -215,3 +215,11 @@ model ProjectItem {
   @@index([chatId])
   @@index([searchId])
 }
+
+// Shared personal read position for the external persistent Pi room.
+// Messages remain in Pi's durable transcript, not duplicated in Sybil Chat.
+model AgentReadState {
+  id        String @id
+  cursor    String @default("0")
+  updatedAt DateTime @updatedAt
+}