fix(messages): peer avatar visibility in chat bubbles

- ConversationsContext: subscribe to profiles UPDATE realtime so
  conversation members[].profile picks up peer avatar / displayName changes
  without a manual refresh
- ConversationPage: skip call_event messages when computing run boundaries.
  Previously a peer bubble followed by a call event from the same sender
  was treated as mid-run -> avatar slot collapsed to a placeholder
- DM peer-profile fallback already added in previous commit covers transient
  member-lookup misses

apps/desktop/src/pages/ConversationPage.tsx

@@ -1,3 +1,4 @@
+import { parseMessagePayload } from '@chat-app/shared/chat';
 import { extractErrorCode } from '@chat-app/shared/i18n';
 import { useCallback, useEffect, useMemo, useRef, useState } from 'react';
 import { useTranslation } from 'react-i18next';
@@ -204,12 +205,26 @@ export function ConversationPage() {
         ) : (
           <ul className="space-y-0.5">
             {messages.map((m, idx) => {
-              const prev = messages[idx - 1];
-              const next = messages[idx + 1];
-              const grouped = idx > 0 && prev?.senderId === m.senderId;
+              // Skip call_event messages when computing run boundaries — they
+              // render as centred separators, not chat bubbles, so they
+              // shouldn't count toward sender continuity. Without this,
+              // a real bubble followed by a call event from the same sender
+              // would be treated as "in the middle of a run" and lose its
+              // avatar.
+              const prev = findAdjacent(messages, idx, -1);
+              const next = findAdjacent(messages, idx, +1);
+              const grouped = !!prev && prev.senderId === m.senderId;
+              // Anchor avatar on the LAST message of a run so it aligns with
+              // the bubble's tail (bottom corner). Tail is bottom-left for
+              // mine, bottom-right for peer — see rounded-[…_4px_…] above.
               const isLastOfRun = !next || next.senderId !== m.senderId;
-              const senderProfile =
+              // DM fallback: if member lookup fails (e.g. transient sync), fall
+              // back to conversation.peer so the peer's avatar still resolves.
+              const memberProfile =
                 conversation?.members.find((mm) => mm.userId === m.senderId)?.profile ?? null;
+              const senderProfile =
+                memberProfile ??
+                (m.senderId !== myId ? (conversation?.peer ?? null) : null);
               return (
                 <li key={m.id}>
                   <MessageBubble
@@ -305,6 +320,25 @@ export function ConversationPage() {
   );
 }
 
+// Walks `messages` from `idx + step` skipping call_event entries until a
+// regular bubble is found or the array boundary is reached. Used to decide
+// run-grouping for avatar placement so call separators don't bleed into
+// sender continuity.
+function findAdjacent<T extends { plaintext: string | null }>(
+  messages: T[],
+  idx: number,
+  step: 1 | -1,
+): T | undefined {
+  let i = idx + step;
+  while (i >= 0 && i < messages.length) {
+    const m = messages[i];
+    if (!m) return undefined;
+    if (parseMessagePayload(m.plaintext).kind !== 'call_event') return m;
+    i += step;
+  }
+  return undefined;
+}
+
 function Banner({ children }: { children: React.ReactNode }) {
   return (
     <div