feat(observability): add exception filter, logging interceptor, and CodeExecutorModule

- add HttpExceptionFilter logging BadRequestException at warn and InternalServerErrorException at error with cause chain
- add LoggingInterceptor logging request/response pairs at debug level with method, path, body, status, and duration
- extract CodeExecutorService into standalone CodeExecutorModule imported by BrowserModule and McpModule
- thread { cause: err } into all catch blocks across auth, browser, and code-executor services

src/interceptors/logging.interceptor.ts

@@ -0,0 +1,31 @@
+import {
+  CallHandler,
+  ExecutionContext,
+  Injectable,
+  Logger,
+  NestInterceptor,
+} from '@nestjs/common';
+import type { Request, Response } from 'express';
+import { Observable, tap } from 'rxjs';
+
+@Injectable()
+export class LoggingInterceptor implements NestInterceptor {
+  private readonly logger = new Logger(LoggingInterceptor.name);
+
+  intercept(context: ExecutionContext, next: CallHandler): Observable<unknown> {
+    const http = context.switchToHttp();
+    const req = http.getRequest<Request>();
+    const res = http.getResponse<Response>();
+    const { method, url, body } = req;
+    const start = Date.now();
+
+    this.logger.debug(`→ ${method} ${url} ${JSON.stringify(body)}`);
+
+    return next.handle().pipe(
+      tap((responseBody) => {
+        const ms = Date.now() - start;
+        this.logger.debug(`← ${method} ${url} ${res.statusCode} (${ms}ms) ${JSON.stringify(responseBody)}`);
+      }),
+    );
+  }
+}