chore(bot): stop sending the unused formattedState with each state frame

The browser bot attached a text rendering of the world state
(formatWorldStateForAgent) to every state message. Nothing reads it: the
gateway forwards only message.state, and the SDK, MCP server and lite runner
never refer to it. Dropping it trims ~5% of each browser bot frame (~10%
after compression).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

server/gateway/types.ts

@@ -13,7 +13,6 @@ import type { BotWorldState, BotAction, ActionResult } from '../../sdk/types';
 export interface BotClientMessage {
     type: 'state' | 'actionResult' | 'setGoal' | 'connected' | 'screenshot_response';
     state?: BotWorldState;
-    formattedState?: string;
     result?: ActionResult;
     actionId?: string;  // Echo back for correlation
     goal?: string;

server/webclient/src/bot/BotOverlay.ts

@@ -5,7 +5,7 @@ import type { Client } from '#/client/Client.js';
 import type { BotState, BotAction, BotWorldState } from './types.js';
 import { BotStateCollector } from './StateCollector.js';
 import { ActionExecutor, formatAction } from './ActionExecutor.js';
-import { formatBotState, formatWorldStateForAgent } from './formatters.js';
+import { formatBotState } from './formatters.js';
 import { GatewayConnection, type GatewayMessageHandler } from './GatewayConnection.js';
 import { OverlayUI } from './OverlayUI.js';
 import { BotActionQueue, type QueuedBotAction } from './ActionQueue.js';
@@ -307,8 +307,7 @@ export class BotOverlay implements GatewayMessageHandler {
         const state = this.collectWorldState();
         if (!state) return;
 
-        const formattedState = formatWorldStateForAgent(state, 'SDK Control');
-        this.gateway.sendState(state, formattedState);
+        this.gateway.sendState(state);
     }
 
     private finishAction(entry: QueuedBotAction, result: ActionResult): void {

server/webclient/src/bot/GatewayConnection.ts

@@ -148,12 +148,11 @@ export class GatewayConnection {
         }
     }
 
-    sendState(state: BotWorldState, formattedState: string): void {
+    sendState(state: BotWorldState): void {
         if (!this.connected) return;
         this.send({
             type: 'state',
-            state,
-            formattedState
+            state
         });
     }