feat(ui/agents): add Conversation pane

Middle pane unioning the initial conversation snapshot with live SSE
events. user_message and assistant_message render as MessageBubble;
tool_call as ToolCallCard; file_diff folds into FilesChangedAccordion.

ui/litellm-dashboard/src/app/(dashboard)/agents/components/three-pane/conversation.tsx

@@ -0,0 +1,114 @@
+"use client";
+
+/**
+ * Conversation — middle pane of the three-pane Session view.
+ *
+ * Renders the union of:
+ *   - the initial conversation snapshot (from /v2/sessions/{sid}/conversation)
+ *   - live events from useSessionEventStream (user_message, assistant_message,
+ *     tool_call, file_diff)
+ *
+ * file_diff events fold into a single "N Files Changed" accordion at the
+ * bottom (cumulative across the run, per the LIT-2881 spec).
+ */
+import { useMemo } from "react";
+import { Empty, Typography } from "antd";
+import MessageBubble from "@/app/(dashboard)/agents/components/three-pane/message-bubble";
+import ToolCallCard from "@/app/(dashboard)/agents/components/three-pane/tool-call-card";
+import FilesChangedAccordion from "@/app/(dashboard)/agents/components/three-pane/files-changed-accordion";
+import Composer from "@/app/(dashboard)/agents/components/three-pane/composer";
+import type {
+  CloudAgentConversationMessage,
+  CloudAgentRunEvent,
+  FileDiffPayload,
+  ToolCallPayload,
+} from "@/types/cloud-agents";
+
+const { Title } = Typography;
+
+interface ConversationProps {
+  sessionId: string;
+  accessToken: string | null;
+  initialMessages: CloudAgentConversationMessage[];
+  events: CloudAgentRunEvent[];
+}
+
+interface DisplayItem {
+  key: string;
+  kind: "message" | "tool_call";
+  message?: CloudAgentConversationMessage;
+  toolCall?: ToolCallPayload;
+}
+
+function buildDisplayItems(
+  initialMessages: CloudAgentConversationMessage[],
+  events: CloudAgentRunEvent[],
+): { items: DisplayItem[]; diffs: FileDiffPayload[] } {
+  const items: DisplayItem[] = initialMessages.map((m) => ({
+    key: `msg-${m.id}`,
+    kind: "message",
+    message: m,
+  }));
+  const diffs: FileDiffPayload[] = [];
+  for (const evt of events) {
+    if (evt.type === "user_message" || evt.type === "assistant_message") {
+      const role = evt.type === "user_message" ? "user" : "assistant";
+      const content = String((evt.payload as { content?: unknown }).content ?? "");
+      items.push({
+        key: `evt-${evt.seq}`,
+        kind: "message",
+        message: {
+          id: `evt-${evt.seq}`,
+          role: role as CloudAgentConversationMessage["role"],
+          content,
+          created_at: evt.created_at,
+        },
+      });
+    } else if (evt.type === "tool_call") {
+      items.push({
+        key: `evt-${evt.seq}`,
+        kind: "tool_call",
+        toolCall: evt.payload as unknown as ToolCallPayload,
+      });
+    } else if (evt.type === "file_diff") {
+      diffs.push(evt.payload as unknown as FileDiffPayload);
+    }
+  }
+  return { items, diffs };
+}
+
+export default function Conversation({ sessionId, accessToken, initialMessages, events }: ConversationProps) {
+  const { items, diffs } = useMemo(() => buildDisplayItems(initialMessages, events), [initialMessages, events]);
+
+  return (
+    <div className="flex h-full flex-col" data-testid="conversation-pane">
+      <div className="border-b border-gray-200 px-4 py-2">
+        <Title level={5} className="!mb-0">
+          Conversation
+        </Title>
+      </div>
+      <div className="flex-1 overflow-y-auto p-4" data-testid="conversation-scroll">
+        {items.length === 0 && diffs.length === 0 ? (
+          <Empty description="No messages yet" />
+        ) : (
+          <>
+            {items.map((it) =>
+              it.kind === "message" && it.message ? (
+                <MessageBubble
+                  key={it.key}
+                  role={it.message.role}
+                  content={it.message.content}
+                  timestamp={it.message.created_at}
+                />
+              ) : it.kind === "tool_call" && it.toolCall ? (
+                <ToolCallCard key={it.key} tool={it.toolCall.tool} input={it.toolCall.input} />
+              ) : null,
+            )}
+            <FilesChangedAccordion diffs={diffs} />
+          </>
+        )}
+      </div>
+      <Composer sessionId={sessionId} accessToken={accessToken} />
+    </div>
+  );
+}