refactor(ui): improve footer controls layout and add scroll-to-bottom button

Simplify agent screen layout by removing redundant status bar container and consolidating all footer controls into the input area component. Add smooth fade animations for realtime mode transitions and a floating scroll-to-bottom button for better UX.

Changes:
- Consolidate status bar and controls into AgentInputArea for cleaner layout hierarchy
- Add scroll-to-bottom button to AgentStreamView with fade animations
- Fix realtime controls stacking on non-agent screens
- Add lastActivityAt serialization to MCP server agent responses
- Remove unnecessary layout wrapper in agent screen

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

packages/server/src/server/acp/mcp-server.ts

@@ -37,6 +37,7 @@ function serializeAgentInfo(info: any): any {
   return {
     ...info,
     createdAt: info.createdAt.toISOString(),
+    lastActivityAt: info.lastActivityAt.toISOString(),
   };
 }
 
@@ -212,6 +213,7 @@ export async function createAgentMcpServer(
             id: z.string(),
             status: z.string(),
             createdAt: z.string(),
+            lastActivityAt: z.string(),
             type: z.literal("claude"),
             sessionId: z.string().nullable(),
             error: z.string().nullable(),
@@ -260,6 +262,7 @@ export async function createAgentMcpServer(
             id: z.string(),
             status: z.string(),
             createdAt: z.string(),
+            lastActivityAt: z.string(),
             type: z.literal("claude"),
             sessionId: z.string().nullable(),
             error: z.string().nullable(),