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/auth/auth.service.ts

@@ -60,8 +60,8 @@ export class AuthService {
     let descriptor: KeyDescriptor;
     try {
       descriptor = JSON.parse(fs.readFileSync(keyJsonPath, 'utf-8'));
-    } catch {
-      throw new BadRequestException(`Cannot read key descriptor: ${keyId}`);
+    } catch (err) {
+      throw new BadRequestException(`Cannot read key descriptor: ${keyId}`, { cause: err });
     }
 
     const keyFilePath = path.resolve(this.keysDir, descriptor.keyFile);
@@ -130,6 +130,7 @@ export class AuthService {
       this.logger.error(`Login failed: ${(err as Error).message}`);
       throw new InternalServerErrorException(
         `Login automation failed: ${(err as Error).message}`,
+        { cause: err },
       );
     } finally {
       await browser.close();