Reduce unnecessary re-renders in agent panel and input components

Narrow zustand selectors to only subscribe to fields each component
actually uses. Split nested objects (availableModes, projectPlacement)
into separate selectors with structural equality checks. Remove the
updatedAt processing-spinner hack in agent-input-area — the server
already guarantees agent status is "running" before ACKing the send
request, so isProcessing can clear on submit success directly.

packages/app/src/hooks/use-agent-screen-state-machine.ts

@@ -1,5 +1,17 @@
 import { useRef } from "react";
-import type { Agent } from "@/contexts/session-context";
+
+export interface AgentScreenAgent {
+  serverId: string;
+  id: string;
+  status: "initializing" | "idle" | "running" | "error" | "closed";
+  cwd: string;
+  projectPlacement?: {
+    checkout?: {
+      cwd?: string;
+      isGit?: boolean;
+    };
+  } | null;
+}
 
 export type AgentScreenMissingState =
   | { kind: "idle" }
@@ -8,8 +20,8 @@ export type AgentScreenMissingState =
   | { kind: "error"; message: string };
 
 export interface AgentScreenMachineInput {
-  agent: Agent | null;
-  placeholderAgent: Agent | null;
+  agent: AgentScreenAgent | null;
+  placeholderAgent: AgentScreenAgent | null;
   missingAgentState: AgentScreenMissingState;
   isConnected: boolean;
   isArchivingCurrentAgent: boolean;
@@ -31,7 +43,7 @@ export type AgentScreenToastLatch = "none" | "history_refresh" | "sync_error";
 
 export interface AgentScreenMachineMemory {
   hasRenderedReady: boolean;
-  lastReadyAgent: Agent | null;
+  lastReadyAgent: AgentScreenAgent | null;
   activeToastLatch: AgentScreenToastLatch;
   hadInitialSyncFailure: boolean;
 }
@@ -70,7 +82,7 @@ export type AgentScreenViewState =
     }
   | {
       tag: "ready";
-      agent: Agent;
+      agent: AgentScreenAgent;
       source: "authoritative" | "optimistic" | "stale";
       sync: AgentScreenReadySyncState;
       isArchiving: boolean;