chore(mcp): remove unused running tool state (#44082)

Co-authored-by: microsoft-playwright-automation[bot] <203992400+microsoft-playwright-automation[bot]@users.noreply.github.com>
Co-authored-by: Yury Semikhatsky <yurys@chromium.org>

Author: microsoft-playwright-automation[bot]

packages/playwright-core/src/tools/backend/browserBackend.ts

@@ -126,7 +126,6 @@ export class BrowserBackend extends EventEmitter<{ disconnected: [], dynamictool
     const cwd = rawArguments._meta?.cwd;
     const raw = !!rawArguments._meta?.raw;
     const response = new Response(context, name, parsedArguments, { relativeTo: cwd, raw, json, commandName });
-    context.setRunningTool(name);
     let responseObject: mcpServer.CallToolResult & { isClose?: boolean };
     try {
       await handle(parsedArguments, response);
@@ -138,8 +137,6 @@ export class BrowserBackend extends EventEmitter<{ disconnected: [], dynamictool
       const message = context.config.skillMode && error instanceof Error ? error.message : String(error);
       const messages = [message, ...context.drainPendingUnhandledRejections().filter(reason => reason !== error).map(formatRejectionReason)];
       responseObject = formatError(messages.join('\n\n'));
-    } finally {
-      context.setRunningTool(undefined);
     }
     if (this._disconnected || responseObject.isClose) {
       delete responseObject.isClose;

packages/playwright-core/src/tools/backend/context.ts

@@ -139,7 +139,6 @@ export class Context {
   private _webmcpToolsSignature = '';
   private _redactUrlParamsRegex: RegExp | undefined;
 
-  private _runningToolName: string | undefined;
   private _pendingUnhandledRejections: unknown[] = [];
   private _unhandledRejectionListeners = new Set<(reason: unknown) => void>();
   private _onUnhandledRejection = (reason: unknown) => {
@@ -434,14 +433,6 @@ export class Context {
     return toRemove.length;
   }
 
-  isRunningTool() {
-    return this._runningToolName !== undefined;
-  }
-
-  setRunningTool(name: string | undefined) {
-    this._runningToolName = name;
-  }
-
   private async _setupRequestInterception(context: playwrightTypes.BrowserContext, disposables: Disposable[]) {
     if (this.config.network?.allowedOrigins?.length) {
       disposables.push(await context.route('**', route => route.abort('blockedbyclient')));