Partial fix for https://github.com/microsoft/playwright/issues/6319
After this fix, the following scenario won't leak and the context state
(cookies, storage, etc) can be reused by the new page sessions:
```js
for (let i = 0; i < 1000; ++i) {
const page = await context.newPage();
await page.goto('...');
await page.close('...');
}
```
53bf1995db
