…ning/closing left panel (elastic#210225)

## Summary

We recently improved the expandable flyout by adding support for a
[fully resizable flyout](elastic#192906).
This work introduce a minor inconvenience, where the right panel gets
re-rendered every time the user expands or collapses the flyout.

This PR fixes this issue by better using the EUI resizable container
(see how to externally control a resizable container
[here](https://eui.elastic.co/#/layout/resizable-container#collapsible-panels-with-external-control)).
The flyout is now always showing a resizable container (even in
collapsed mode) but EUI manages internally hiding the left section and
the resize button.

#### Old behavior

https://github.com/user-attachments/assets/4d7589ec-0edf-4690-9ce4-7b969ae0bb44

#### New behavior

https://github.com/user-attachments/assets/7cf720b8-5b31-4cc9-b213-21472ea880d6

The rest of the flyout's behavior remains untouched:
- identical default widths
- user selected widths are still applied
- no changes to the preview behavior

### Checklist

- [ ] [Unit or functional
tests](https://www.elastic.co/guide/en/kibana/master/development-tests.html)
were updated or added to match the most common scenarios

(cherry picked from commit 7a9bf13)