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('...');
}
```
- When disposing recursively, only the root dispatcher received
`_dispose()` call, while some dispatchers need `_onDispose()` to clean
things up.
- When reusing the context, pages should be notified with `_onClose()`
so that all client-side waiting promises could reject.
Fixes#19216.
Previously, we only validated/converted on the way to the server,
but not from the server.
Validating both ways catches issues earlier, and allows us to
perform automatic conversions, for example only converting
buffers to base64 when sending over wire.
