[Epic] Server side rendering / SSR

Issue description updated by @tkajtoch.

## Related

Next.js Support: https://github.com/elastic/eui/issues/8881

## Summary

Server Side Rendering (SSR) isn't currently officially supported by EUI despite the effort made in the past to make it so. We know that some internal and external teams already use our components and utilities on the server side, and we want to provide official support for this feature.

We've already made some improvements in the past and fixed reported bugs related to SSR as they came, but we have yet to take the time and effort to confirm EUI is 100% SSR compatible.

## Acceptance Criteria

* All EUI components should be SSR compatible
* There should be no hydration errors related to unique ID generation, DOM nesting, and others when rendering EUI components
* A documentation page should be added to guide users on how to use EUI in server-side rendered environments as well as in Next.js

- [x] https://github.com/elastic/eui/issues/5418
- [x] https://github.com/elastic/eui/issues/5305
- [ ] https://github.com/elastic/eui/issues/7078