fix: preserve err.code in SerializedError cross-process serialization

[Wu Shuwen (dajiaohuang)]

Summary

APIRequestContext errors were losing the err.code structured field after cross-process serialization.

Root Cause

serializeError in both client/errors.ts and server/errors.ts only preserved message, stack, and name from error objects. The code field (common in Node.js network errors like ECONNREFUSED, ECONNRESET, etc.) was silently dropped.

Fix

1. Added code?: string to the SerializedError.error type in packages/protocol/src/structs.d.ts
2. Updated serializeError in both client and server to include e.code when present
3. Updated parseError in both client and server to restore the code field on the deserialized error

Testing

This fix can be verified with the reproduction script from issue #42532:

import { request } from '@playwright/test'

const context = await request.newContext()
try {
  await context.post('http://127.0.0.1:1/', { data: {} })
} catch (err) {
  console.log('code:', err.code)  // Now properly shows 'ECONNREFUSED'
}

Related Issue

Fixes #42532

[Dmitry Gozman (dgozman)]

Closing in favor of #42562.