dillon1000/react

Add ReactDOMClient to ServerIntegration(Hooks|NewContext) (#28135)

## Overview

Branched off https://github.com/facebook/react/pull/28130

### ~Failing~ Fixed by @eps1lon 
Most of the tests pass, but there are 3 tests that have additional
warnings due to client render error retries.

For example, before we would log:

```
Warning: Do not call Hooks inside useEffect(...), useMemo(...), or other built-in Hooks.
Warning: Expected server HTML to contain a matching text node for "0" in <div>.
```

And now we log

```
Warning: Do not call Hooks inside useEffect(...), useMemo(...), or other built-in Hooks.
Warning: Expected server HTML to contain a matching text node for "0" in <div>.
Warning: Do not call Hooks inside useEffect(...), useMemo(...), or other built-in Hooks.
```

We can't just update the expected error count for these tests, because
the additional error only happens on the client. So I need some guidance
on how to fix these.

---------

Co-authored-by: Sebastian Silbermann <[email protected]>